Showing 1–50 of 240 results for author: Bambi, C

Zero-point length as a topological protection of black hole regularity

Authors: Ankit Anand, Kimet Jusufi, Cosimo Bambi

Abstract: We investigate the thermodynamic topology of regular black holes with zero-point length using an extended first law that includes the zero-point length stored in the geometry. By treating the regularization scale $l_0$ as a thermodynamic variable, we analyze the Hessian geometry of the thermodynamic manifold and demonstrate that the vector field $\vecφ = (T, Ψ)$, where $T$ is the temperature and… ▽ More We investigate the thermodynamic topology of regular black holes with zero-point length using an extended first law that includes the zero-point length stored in the geometry. By treating the regularization scale $l_0$ as a thermodynamic variable, we analyze the Hessian geometry of the thermodynamic manifold and demonstrate that the vector field $\vecφ = (T, Ψ)$, where $T$ is the temperature and $Ψ$ is the conjugate to $l_0$, never vanishes in the physical parameter space for $l_0 > 0$. This implies the absence of Morse critical points and a vanishing winding number ($W = 0$), indicating topological protection against the formation of naked singularities. Crucially, we show that in the singular limit $l_0 \to 0$, a non-zero winding number ($W = 1$) emerges, characterizing the Schwarzschild singularity as a topological defect. The conservation of this topological invariant under smooth evolution provides a rigorous topological formulation of the weak cosmic censorship conjecture: the presence of zero-point length not only regularizes the spacetime background but also enforces topological protection against the formation of singularities, preventing black hole-to-naked singularity transitions. △ Less

Submitted 2 March, 2026; originally announced March 2026.

Comments: 11 pages, 2 figures

Testing non-circular black hole spacetime with X-ray reflection

Authors: Leda Gao, Swarnim Shashank, Cosimo Bambi

Abstract: X-ray reflection spectroscopy is a powerful tool for testing the Kerr hypothesis and probing the strong gravity regime around accreting black holes. Most tests of General Relativity (GR) assume that the spacetime around a black hole is circular, meaning the metric possesses a specific symmetry structure common to the Kerr solution. However, deviations from circularity are predicted by various modi… ▽ More X-ray reflection spectroscopy is a powerful tool for testing the Kerr hypothesis and probing the strong gravity regime around accreting black holes. Most tests of General Relativity (GR) assume that the spacetime around a black hole is circular, meaning the metric possesses a specific symmetry structure common to the Kerr solution. However, deviations from circularity are predicted by various modified gravity theories and non-vacuum General Relativity solutions. In this work, we test a specific non-circular metric constructed based on a locality principle, where the deviation from the Kerr spacetime is driven by the local spacetime curvature. To accurately model the reflection spectrum in this background, we implement a relativistic ray-tracing code in horizon-penetrating (ingoing Kerr) coordinates, which are favored for their ability to avoid introducing curvature singularities at the horizon in non-circular spacetimes. We apply this model to the high-quality \textit{NuSTAR} spectrum of the Galactic black hole binary EXO 1846--031. Our spectral analysis reveals a source with a high inclination angle ($ι\approx 76^{\circ}$) and a near-extremal spin parameter ($a_* \approx 0.98$). While we identify a global minimum in the parameter space suggesting a non-zero deformation ($\ell_{\mathrm{NP}} \approx 0.12$), the 99\% confidence interval fully encompasses the Kerr limit ($\ell_{\mathrm{NP}}=0$). We conclude that the current X-ray reflection data for EXO 1846--031 are consistent with the Kerr hypothesis. This work demonstrates the feasibility of using X-ray reflection spectroscopy to constrain non-circular metrics and establishes a framework for future tests. △ Less

Submitted 18 February, 2026; originally announced February 2026.

Comments: 13 pages, 6 figures

Searching for Isolated Black Hole Candidates within 15 pc of the Solar System in Gaia DR3

Authors: Abdurakhmon Nosirov, Cosimo Bambi, Leda Gao, Jos de Bruijne, Jiachen Jiang, Andrea Santangelo, Fu-Guo Xie

Abstract: Theoretical models predict that the Galaxy hosts $10^8$-$10^9$ black holes formed from the complete gravitational collapse of heavy stars and that most of these black holes are isolated, without any companion. Within 15 pc of the Solar System ($\sim 50$ ly), there may be a few black holes. If located inside one of the Local Interstellar Clouds - which occupy 5-20% of this local volume - an isolate… ▽ More Theoretical models predict that the Galaxy hosts $10^8$-$10^9$ black holes formed from the complete gravitational collapse of heavy stars and that most of these black holes are isolated, without any companion. Within 15 pc of the Solar System ($\sim 50$ ly), there may be a few black holes. If located inside one of the Local Interstellar Clouds - which occupy 5-20% of this local volume - an isolated black hole could produce detectable electromagnetic emission via accretion from the interstellar medium, given the capabilities of current or near-future observatories. However, precise predictions remain challenging due to large uncertainties in the expected accretion spectra. Outside these clouds, the accretion rate would be too low in any standard model to yield a detectable electromagnetic signal. While astrometric detection via gravitational perturbation of nearby stars is conceivable, the local stellar density is too low for this method to be realistically successful. We have searched the Gaia DR3 catalog for candidate isolated black holes accreting from the interstellar medium and identified five sources. All candidates lie close to the Galactic plane, making them likely spurious astrometric solutions, for instance caused by unmodelled background sources (crowding) and/or unmodelled binarity; nevertheless, they cannot be definitively ruled out without follow-up observations. △ Less

Submitted 20 January, 2026; originally announced January 2026.

Comments: 10 pages, 5 figures

Taming singularities and chaos in conformal gravity

Authors: Jiale Gu, Leonardo Modesto, Cosimo Bambi

Abstract: We hereby address the cosmological singularity problem in a general gravitational theory invariant under Weyl conformal transformations. In particular, we focus on the Bianchi IX spacetime and we show that both the initial (big bang) and final (big crunch) singularities disappear in an infinite class of conformal frames naturally selected according to analyticity. It turns out that the past and fu… ▽ More We hereby address the cosmological singularity problem in a general gravitational theory invariant under Weyl conformal transformations. In particular, we focus on the Bianchi IX spacetime and we show that both the initial (big bang) and final (big crunch) singularities disappear in an infinite class of conformal frames naturally selected according to analyticity. It turns out that the past and future singularities are both unattainable within a finite affine parameter (for massless particles) or within a finite proper time (for massive and conformally coupled particles). In order to prove such a statement, we show the geodesic completion of the spacetime when probed by massless, massive, and conformally coupled particles. Finally, the chaotic behavior of the spacetime near the singularity is tamed by a conformal rescaling that turns the Bianchi IX metric into a quasi-FLRW spacetime. △ Less

Submitted 20 January, 2026; v1 submitted 1 November, 2025; originally announced November 2025.

Comments: 12 pages, no figures. v2: refereed version

Journal ref: Eur. Phys. J. C (2026) 86:42

Testing black hole metrics with binary black hole inspirals

Authors: Zhe Zhao, Swarnim Shashank, Debtroy Das, Cosimo Bambi

Abstract: Gravitational wave astronomy has opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. In this study, we examine a series of well-motivated deviations from the classical Kerr solution of General Relativity and employ gravitational wave data to place constraints on possible deviations from the Kerr geometry. The method involves calculating the phas… ▽ More Gravitational wave astronomy has opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. In this study, we examine a series of well-motivated deviations from the classical Kerr solution of General Relativity and employ gravitational wave data to place constraints on possible deviations from the Kerr geometry. The method involves calculating the phase of gravitational waves using the effective one-body formalism and then applying the parameterized post-Einsteinian framework to constrain the parameters appearing in these scenarios beyond General Relativity. The effective one-body method, known for its capability to model complex gravitational waveforms, is used to compute the wave phase, and the post-Einsteinian framework allows for a flexible, model-independent approach to parameter estimation. We demonstrate that gravitational wave data provide evidence supporting the Kerr nature of black holes, showing no significant deviations from General Relativity, thereby affirming its validity within the current observational limits. We further assess the potential impact of orbital eccentricity and find that, within observationally allowed ranges, its contribution to the inferred deviations is subdominant. This work bridges theoretical waveform modeling with observational constraints, providing a pathway to test the no-hair theorem and probe the astrophysical viability of modified black holes. △ Less

Submitted 6 April, 2026; v1 submitted 6 October, 2025; originally announced October 2025.

Comments: 28 pages, 1 figure. v2: refereed version

Journal ref: Physics of the Dark Universe 52 (2026) 102297

An interstellar mission to the closest black hole?

Authors: Cosimo Bambi

Abstract: In this manuscript, I discuss the possibility of sending a small probe to the closest black hole with the goal of addressing some fundamental questions of modern physics. Are astrophysical black holes the Kerr black holes predicted by General Relativity? Do astrophysical black holes have an event horizon? Is the physics around a black hole the same physics as in our laboratories on Earth? While we… ▽ More In this manuscript, I discuss the possibility of sending a small probe to the closest black hole with the goal of addressing some fundamental questions of modern physics. Are astrophysical black holes the Kerr black holes predicted by General Relativity? Do astrophysical black holes have an event horizon? Is the physics around a black hole the same physics as in our laboratories on Earth? While we do not have the technology for a similar mission today, it may be available in the next 20-30 years. The whole mission may last up to a century (depending on the actual distance of the black hole and the speed of the probe), but it may represent a unique opportunity to perform precise and accurate tests of General Relativity in the strong field regime. △ Less

Submitted 14 September, 2025; originally announced September 2025.

Comments: 6 pages, 2 figures. Talk given at the 22nd Lomonosov Conference on Elementary Particle Physics, 21-27 August 2025, Moscow, Russia

Testing General Relativity with Black Holes

Authors: Cosimo Bambi

Abstract: The theory of General Relativity has successfully passed a large number of observational tests. The theory has been extensively tested in the weak-field regime with experiments in the Solar System and observations of binary pulsars. The past 10 years have seen significant advancements in the study of the strong-field regime, which can now be tested with gravitational waves, X-ray data, and black h… ▽ More The theory of General Relativity has successfully passed a large number of observational tests. The theory has been extensively tested in the weak-field regime with experiments in the Solar System and observations of binary pulsars. The past 10 years have seen significant advancements in the study of the strong-field regime, which can now be tested with gravitational waves, X-ray data, and black hole imaging. Here I summarize the state-of-the-art of the tests of General Relativity with black hole X-ray data and I briefly discuss the long-term vision of the possibility of an interstellar mission to the closest black hole for more precise and accurate tests. △ Less

Submitted 28 January, 2026; v1 submitted 17 August, 2025; originally announced August 2025.

Comments: 9 pages, 2 figures. v2: refereed version. Talk given at the International Conference on Theoretical Physics and Astrophysics (ICTPA-2025), 24-28 March 2025, Tashkent, Uzbekistan

Probing missing physics from inspiralling compact binaries via time-frequency tracks

Authors: Debtroy Das, Soumen Roy, Anand S. Sengupta, Cosimo Bambi

Abstract: The orbital evolution of binary black hole (BBH) systems is determined by the component masses and spins of the black holes and the governing gravity theory. Gravitational wave (GW) signals from the evolution of BBH orbits offer an unparalleled opportunity for examining the predictions of General Relativity (GR) and for searching for missing physics in the current waveform models. We present a met… ▽ More The orbital evolution of binary black hole (BBH) systems is determined by the component masses and spins of the black holes and the governing gravity theory. Gravitational wave (GW) signals from the evolution of BBH orbits offer an unparalleled opportunity for examining the predictions of General Relativity (GR) and for searching for missing physics in the current waveform models. We present a method of stacking up the time-frequency pixel energies through the orbital frequency evolution with the flexibility of gradually shifting the orbital frequency curve along the frequency axis. We observe a distinct energy peak corresponding to the GW signal's quadrupole mode. If an alternative theory of gravity is considered and the analysis of the BBH orbital evolution is executed following GR, the energy distribution on the time-frequency plane will be significantly different. We propose a new consistency test to check whether our theoretical waveform explains the BBH orbital evolution. Through the numerical simulation of beyond-GR theory of gravity and utilizing the framework of second-generation interferometers, we demonstrate the efficiency of this new method in detecting any possible departure from GR. Finally, when applied to an eccentric BBH system and GW190814, which shows the signatures of higher-order multipoles, our method provides an exquisite probe of missing physics in the GR waveform models. △ Less

Submitted 29 July, 2025; originally announced July 2025.

Comments: 15 pages, 9 figures

Stellar-Mass Black Holes

Authors: Cosimo Bambi

Abstract: Stellar-mass black holes ($3$ $M_\odot \lesssim M_{\rm BH} \lesssim 150$ $M_\odot$) are the natural product of the evolution of heavy stars ($M_{\rm star} \gtrsim 20$ $M_\odot$). In our Galaxy, we expect $10^8$-$10^9$ stellar-mass black holes formed from the gravitational collapse of heavy stars, but currently we know fewer than 100 objects. We also know $\sim 100$ stellar-mass black holes in othe… ▽ More Stellar-mass black holes ($3$ $M_\odot \lesssim M_{\rm BH} \lesssim 150$ $M_\odot$) are the natural product of the evolution of heavy stars ($M_{\rm star} \gtrsim 20$ $M_\odot$). In our Galaxy, we expect $10^8$-$10^9$ stellar-mass black holes formed from the gravitational collapse of heavy stars, but currently we know fewer than 100 objects. We also know $\sim 100$ stellar-mass black holes in other galaxies, most of them discovered by gravitational wave observatories in the past 10 years. The detection of black holes is indeed extremely challenging and possible only in very special cases. This article is a short review on the physics and astrophysics of stellar-mass black holes, including Galactic and extragalactic black holes in X-ray binaries, black holes in astrometric binaries, isolated black holes, and black holes in compact binaries. The article also addresses some important open issues and introduces the idea of a possible interstellar mission to the closest black hole. △ Less

Submitted 26 August, 2025; v1 submitted 21 July, 2025; originally announced July 2025.

Comments: 21 pages, 7 figures. Invited review article for a special issue of Symmetry. v2: refereed version

Journal ref: Symmetry 17: 1393 (2025)

Measuring black hole spins with x-ray reflection spectroscopy: A GRMHD outlook

Authors: Swarnim Shashank, Askar B. Abdikamalov, Honghui Liu, Abdurakhmon Nosirov, Cosimo Bambi, Indu K. Dihingia, Yosuke Mizuno

Abstract: X-ray reflection spectroscopy has evolved as one of the leading methods to measure black hole spins. However, the question is whether its measurements are subjected to systematic biases, especially considering the possible discrepancy between the spin measurements inferred with this technique and those from gravitational wave observations. In this work, we use general relativistic magnetohydrodyna… ▽ More X-ray reflection spectroscopy has evolved as one of the leading methods to measure black hole spins. However, the question is whether its measurements are subjected to systematic biases, especially considering the possible discrepancy between the spin measurements inferred with this technique and those from gravitational wave observations. In this work, we use general relativistic magnetohydrodynamic (GRMHD) simulations of thin accretion disks around spinning black holes for modeling the accretion process, and then we simulate NuSTAR observations to test the capability of modern reflection models in recovering the input spins. For the first time, we model the electron density and ionization profiles from GRMHD-simulated disks. Our study reveals that current reflection models work well only for fast-rotating black holes. We model the corona as the base of the jet and we find that reflection models with lamppost emissivity profiles fail to recover the correct black hole spins. Reflection models with broken power-law emissivity profiles perform better. As we increase the complexity of the simulated models, it is more difficult to recover the correct input spins, pointing toward the need to update our current reflection models with more advanced accretion disks and coronal geometries. △ Less

Submitted 21 December, 2025; v1 submitted 3 July, 2025; originally announced July 2025.

Comments: 21 pages, 12 figures. v2: refereed version. Supplemental material available at http://link.aps.org/supplemental/10.1103/4sth-rnwv

Journal ref: Phys. Rev. D 112, 123030 (2025)

Exploring black hole shadows in axisymmetric spacetimes with coordinate-independent methods and neural networks

Authors: Temurbek Mirzaev, Bobomurat Ahmedov, Cosimo Bambi

Abstract: The study of black hole shadows provides a powerful tool for testing the predictions of general relativity and exploring deviations from the standard Kerr metric in the strong gravitational field regime. Here, we investigate the shadow properties of axisymmetric gravitational compact objects using a coordinate-independent formalism. We analyze black hole shadows in various spacetime geometries, in… ▽ More The study of black hole shadows provides a powerful tool for testing the predictions of general relativity and exploring deviations from the standard Kerr metric in the strong gravitational field regime. Here, we investigate the shadow properties of axisymmetric gravitational compact objects using a coordinate-independent formalism. We analyze black hole shadows in various spacetime geometries, including the Kerr, Taub-NUT, $γ$, and Kaluza-Klein metrics, to identify distinctive features that can be used to constrain black hole parameters. To achieve a more robust characterization, we employ both Legendre and Fourier expansions, demonstrating that the Fourier approach may offer better coordinate independence and facilitate cross-model comparisons. Finally, we develop a machine learning framework based on neural networks trained on synthetic shadow data, enabling precise parameter estimation from observational results. Using data from observational astronomical facilities such as the Event Horizon Telescope (EHT), Keck, and the Very Large Telescope Interferometer (VLTI), we provide constraints on black hole parameters derived from shadow observations. Our findings highlight the potential of coordinate-independent techniques and machine learning for advancing black hole astrophysics and testing fundamental physics beyond general relativity. △ Less

Submitted 12 November, 2025; v1 submitted 3 July, 2025; originally announced July 2025.

Comments: Revised version after referee report. Accepted for publication in The European Physical Journal C (EPJC), 2025

MSC Class: 83C57; 85A99; 68T07

Journal ref: Eur. Phys. J. C 85, 945 (2025)

Probing the Strong Gravity Region of Black Holes with eXTP

Authors: Qingcui Bu, Cosimo Bambi, Lijun Gou, Yanjun Xu, Phil Uttley, Alessandra De Rosa, Andrea Santangelo, Silvia Zane, Hua Feng, Shuang-Nan Zhang, Chichuan Jin, Haiwu Pan, Xinwen Shu, Francesco Ursini, Yanan Wang, Jianfeng Wu, Bei You, Yefei Yuan, Wenda Zhang, Stefano Bianchi, Lixin Dai, Tiziana Di Salvo, Michal Dovciak, Yuan Feng, Hengxiao Guo , et al. (20 additional authors not shown)

Abstract: We present the novel capabilities of the enhanced X-ray Timing and Polarimetry (eXTP) mission to study the strong gravity region around stellar-mass black holes in X-ray binary systems and supermassive black holes in active galactic nuclei. eXTP can combine X-ray spectral, timing, and polarimetric techniques to study the accretion process near black holes, measure black hole masses and spins, and… ▽ More We present the novel capabilities of the enhanced X-ray Timing and Polarimetry (eXTP) mission to study the strong gravity region around stellar-mass black holes in X-ray binary systems and supermassive black holes in active galactic nuclei. eXTP can combine X-ray spectral, timing, and polarimetric techniques to study the accretion process near black holes, measure black hole masses and spins, and test Einstein's theory of General Relativity in the strong field regime. We show how eXTP can improve the current measurements of black holes of existing X-ray missions and we discuss the scientific questions that can be addressed. △ Less

Submitted 8 September, 2025; v1 submitted 9 June, 2025; originally announced June 2025.

Comments: accepted for publication in the SCIENCE CHINA Physics, Mechanics & Astronomy

Black hole mimickers: from theory to observation

Authors: Cosimo Bambi, Ramy Brustein, Vitor Cardoso, Andrew Chael, Ulf Danielsson, Suvendu Giri, Anuradha Gupta, Pierre Heidmann, Luis Lehner, Steven Liebling, Andrea Maselli, Elisa Maggio, Samir Mathur, Lia Medeiros, Alex B. Nielsen, Héctor R. Olivares-Sánchez, Paolo Pani, Nils Siemonsen, George N. Wong

Abstract: The black hole paradigm, while remarkably successful, raises fundamental questions-both classical and quantum-about the nature of spacetime, horizons, and singularities. Black hole mimickers, horizonless ultra-compact objects, have emerged as potential alternatives that seek to resolve some of these puzzles while remaining consistent with current observational constraints. Recent breakthroughs in… ▽ More The black hole paradigm, while remarkably successful, raises fundamental questions-both classical and quantum-about the nature of spacetime, horizons, and singularities. Black hole mimickers, horizonless ultra-compact objects, have emerged as potential alternatives that seek to resolve some of these puzzles while remaining consistent with current observational constraints. Recent breakthroughs in gravitational-wave astronomy and horizon-scale electromagnetic imaging have opened new avenues to test this paradigm-making this an opportune moment to systematically investigate such alternatives. This vision document presents a snapshot of the field as discussed at the Black Hole Mimickers: From Theory to Observation workshop, where experts from gravitational wave astronomy, very long baseline interferometry, numerical and mathematical relativity, and high-energy physics converged to assess the current frontiers. By highlighting key open questions and proposing concrete pathways forward, this document aims to guide future efforts to probe the nature of compact objects. As the field stands at the crossroads of theoretical innovation and observational breakthroughs, we outline strategies to harness upcoming observational capabilities to fundamentally test the black hole paradigm. △ Less

Submitted 13 May, 2025; originally announced May 2025.

Comments: Proceedings of the "Black Hole Mimickers: From Theory to Observation" workshop organized at the Princeton Center for Theoretical Sciences (PCTS), Princeton University, NJ, USA from March 3-5 2025

An interstellar mission to test astrophysical black holes

Authors: Cosimo Bambi

Abstract: Black holes are the sources of the strongest gravitational fields that can be found today in the Universe and are ideal laboratories for testing Einstein's theory of General Relativity in the strong field regime. In this letter, I show that the possibility of an interstellar mission to send a small spacecraft to the nearest black hole, although very speculative and extremely challenging, is not co… ▽ More Black holes are the sources of the strongest gravitational fields that can be found today in the Universe and are ideal laboratories for testing Einstein's theory of General Relativity in the strong field regime. In this letter, I show that the possibility of an interstellar mission to send a small spacecraft to the nearest black hole, although very speculative and extremely challenging, is not completely unrealistic. Certainly we do not have the necessary technology today, but it may be available in the next 20-30 years. The mission may last 80-100 years, but we would be able to obtain very valuable information about black holes and General Relativity that might be difficult to obtain in other ways. △ Less

Submitted 13 August, 2025; v1 submitted 20 April, 2025; originally announced April 2025.

Comments: 18 pages, 4 figures. v2: refereed version

Journal ref: iScience 28, 113142 (2025)

Quasi-normal modes of slowly-rotating Johannsen black holes

Authors: Yuhao Guo, Swarnim Shashank, Cosimo Bambi

Abstract: The detection of gravitational waves with ground-based laser interferometers has opened a new window to test and constrain General Relativity (GR) in the strong, dynamical, and non-linear regime. In this paper, we follow an agnostic approach and we study the quasi-normal modes of gravitational perturbations of Johannsen black holes under the assumptions of the validity of the Einstein Equations an… ▽ More The detection of gravitational waves with ground-based laser interferometers has opened a new window to test and constrain General Relativity (GR) in the strong, dynamical, and non-linear regime. In this paper, we follow an agnostic approach and we study the quasi-normal modes of gravitational perturbations of Johannsen black holes under the assumptions of the validity of the Einstein Equations and of low values of the black hole spin parameter and deformation parameters. We find that the deformation parameter $α_{13}$ has a stronger impact on the quasi-normal modes than the other leading order deformation parameters ($α_{22}$, $α_{52}$, and $ε_{3}$). We derive a fitting formula for the fundamental modes with $l=2$ and $l=3$ for the deformation parameter $α_{13}$ valid in the slow rotation approximation ($a_* < 0.4$). Finally, we constrain $α_{13}$ from the event GW170104; within our analysis, we find that the data of GW170104 are consistent with the predictions of GR. △ Less

Submitted 17 April, 2025; v1 submitted 11 December, 2024; originally announced December 2024.

Comments: 17 pages, 7 figures. v2: refereed version

Journal ref: Eur. Phys. J. C (2025) 85:425

About the accuracy of the relxill/relxill_nk models in view of the next generation of X-ray missions

Authors: Honghui Liu, Askar B. Abdikamalov, Temurbek Mirzaev, Cosimo Bambi, Thomas Dauser, Javier A. Garcia, Zuobin Zhang

Abstract: X-ray reflection spectroscopy is a powerful tool to study the strong gravity region of black holes. The next generation of astrophysical X-ray missions promises to provide unprecedented high-quality data, which could permit us to get very precise measurements of the properties of the accretion flow and of the spacetime geometry in the strong gravity region around these objects. In this work, we te… ▽ More X-ray reflection spectroscopy is a powerful tool to study the strong gravity region of black holes. The next generation of astrophysical X-ray missions promises to provide unprecedented high-quality data, which could permit us to get very precise measurements of the properties of the accretion flow and of the spacetime geometry in the strong gravity region around these objects. In this work, we test the accuracy of the relativistic calculations of the reflection model relxill and of its extension to non-Kerr spacetimes relxill_nk in view of the next generation of X-ray missions. We simulate simultaneous observations with Athena/X-IFU and LAD of bright Galactic black holes with a precise and accurate ray-tracing code and we fit the simulated data with the latest versions of relline and relline_nk. While we always recover the correct input parameters, we find residuals in the fits when the emission from the inner part of the accretion disk is higher. Such residuals disappear if we increase the number of interpolation points on the disk in the integral of the transfer function. We also simulate full reflection spectra and find that the emission angle from the accretion disk should be treated properly in this case. △ Less

Submitted 29 November, 2024; originally announced December 2024.

Comments: 11 pages, 9 figures

Journal ref: Mon. Not. Roy. Astron. Soc. 536, 2594-2602 (2025)

Towards a new generation of reflection models for precision measurements of accreting black holes

Authors: Cosimo Bambi

Abstract: Blurred reflection features are commonly observed in the X-ray spectra of accreting black holes. In the presence of high-quality data and with the correct astrophysical model, X-ray reflection spectroscopy is a powerful tool to probe the strong gravity region of black holes, study the morphology of the accreting matter, measure black hole spins, and test Einstein's theory of General Relativity in… ▽ More Blurred reflection features are commonly observed in the X-ray spectra of accreting black holes. In the presence of high-quality data and with the correct astrophysical model, X-ray reflection spectroscopy is a powerful tool to probe the strong gravity region of black holes, study the morphology of the accreting matter, measure black hole spins, and test Einstein's theory of General Relativity in the strong field regime. In the past 10-15 years, there has been significant progress in the development of the analysis of these reflection features, thanks to both more sophisticated theoretical models and new observational data. However, the next generation of X-ray missions (e.g. eXTP, Athena, HEX-P) promises to provide unprecedented high-quality data, which will necessarily require more accurate synthetic reflection spectra than those available today. In this talk, I will review the state-of-the-art in reflection modeling and I will present current efforts to develop a new generation of reflection models with machine learning techniques. △ Less

Submitted 3 October, 2024; originally announced October 2024.

Comments: 15 pages, 2 figures. Talk given at the workshop "Frontier Research in Astrophysics - IV" (Palermo, Italy, 9-14 September 2024)

Journal ref: PoS FRAPWS2024 (2025) 024

Gravitational Wave Astronomy With TianQin

Authors: En-Kun Li, Shuai Liu, Alejandro Torres-Orjuela, Xian Chen, Kohei Inayoshi, Long Wang, Yi-Ming Hu, Pau Amaro-Seoane, Abbas Askar, Cosimo Bambi, Pedro R. Capelo, Hong-Yu Chen, Alvin J. K. Chua, Enrique Condés-Breña, Lixin Dai, Debtroy Das, Andrea Derdzinski, Hui-Min Fan, Michiko Fujii, Jie Gao, Mudit Garg, Hongwei Ge, Mirek Giersz, Shun-Jia Huang, Arkadiusz Hypki , et al. (28 additional authors not shown)

Abstract: The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave sig… ▽ More The opening of the gravitational wave window has significantly enhanced our capacity to explore the universe's most extreme and dynamic sector. In the mHz frequency range, a diverse range of compact objects, from the most massive black holes at the farthest reaches of the Universe to the lightest white dwarfs in our cosmic backyard, generate a complex and dynamic symphony of gravitational wave signals. Once recorded by gravitational wave detectors, these unique fingerprints have the potential to decipher the birth and growth of cosmic structures over a wide range of scales, from stellar binaries and stellar clusters to galaxies and large-scale structures. The TianQin space-borne gravitational wave mission is scheduled for launch in the 2030s, with an operational lifespan of five years. It will facilitate pivotal insights into the history of our universe. This document presents a concise overview of the detectable sources of TianQin, outlining their characteristics, the challenges they present, and the expected impact of the TianQin observatory on our understanding of them. △ Less

Submitted 2 December, 2024; v1 submitted 29 September, 2024; originally announced September 2024.

Comments: TianQin Gravitational Wave Whitepaper, 72 pages, 30 figures

Black hole X-ray spectra: notes on the relativistic calculations

Authors: Cosimo Bambi

Abstract: This is a collection of notes to calculate electromagnetic spectra of geometrically thin and optically thick accretion disks around black holes. The presentation is intentionally pedagogical and most calculations are reported step by step. In the disk-corona model, the spectrum of a source has three components: a thermal component from the disk, a Comptonized component from the corona, and a refle… ▽ More This is a collection of notes to calculate electromagnetic spectra of geometrically thin and optically thick accretion disks around black holes. The presentation is intentionally pedagogical and most calculations are reported step by step. In the disk-corona model, the spectrum of a source has three components: a thermal component from the disk, a Comptonized component from the corona, and a reflection component from the disk. These notes review only the relativistic calculations. The formulas presented here are valid for stationary, axisymmetric, asymptotically-flat, circular spacetimes, so they can be potentially used for a large class of black hole solutions. △ Less

Submitted 22 August, 2024; originally announced August 2024.

Comments: 25 pages, 8 figures. Lecture notes

Observed jet power and radiative efficiency of black hole candidates in Kerr + PFDM model

Authors: Bakhtiyor Narzilloev, Ahmadjon Abdujabbarov, Bobomurat Ahmedov, Cosimo Bambi

Abstract: In this research, we explore the electromagnetic energy emitted by astrophysical black holes within the Kerr+PFDM spacetime, a model encompassing rotating black holes surrounded by dark matter. Our investigation focuses on black holes within X-ray binary systems, namely GRS 1915+105, GRO J1655-40, XTE J1550-564, A0620-00, H1743-322, and GRS 1124-683. Our findings indicate that the Kerr+PFDM spacet… ▽ More In this research, we explore the electromagnetic energy emitted by astrophysical black holes within the Kerr+PFDM spacetime, a model encompassing rotating black holes surrounded by dark matter. Our investigation focuses on black holes within X-ray binary systems, namely GRS 1915+105, GRO J1655-40, XTE J1550-564, A0620-00, H1743-322, and GRS 1124-683. Our findings indicate that the Kerr+PFDM spacetime can account for the radiative efficiency of these sources as determined through the continuum fitting method (CFM). Additionally, employing the Blandford-Znajeck mechanism, we demonstrate the ability to replicate the observed jet power. By combining the outcomes of both analyses for the selected objects, we establish more rigorous constraints on the spacetime parameters. Notably, our results reveal that similar to the Kerr spacetime, the Kerr+PFDM spacetime cannot simultaneously account for the observed jet power and radiative efficiency of GRS 1915+105. △ Less

Submitted 10 August, 2024; originally announced August 2024.

Comments: 13 pages, 9 figures. Accepted in EPJC. arXiv admin note: text overlap with arXiv:2310.10554

Journal ref: Eur. Phys. J. C (2024) 84:909

Testing the Kerr nature with binary black hole inspirals

Authors: Swarnim Shashank, Cosimo Bambi, Rittick Roy

Abstract: The theory of general relativity (GR) is the standard framework for the description of gravitation and the geometric structure of spacetime. With the recent advancement of observational instruments, it has become possible to probe the strong field regime to test GR. We present the constraints obtained from the binary black hole inspiral data of the LIGO-Virgo-Kagra (LVK) gravitational wave (GW) ob… ▽ More The theory of general relativity (GR) is the standard framework for the description of gravitation and the geometric structure of spacetime. With the recent advancement of observational instruments, it has become possible to probe the strong field regime to test GR. We present the constraints obtained from the binary black hole inspiral data of the LIGO-Virgo-Kagra (LVK) gravitational wave (GW) observations on the deformations of some popular parametrized non-Kerr metrics. △ Less

Submitted 17 July, 2024; originally announced July 2024.

Comments: 7 pages, 1 figure. Prepared for the proceeding of the seventh international workshop on the TianQin science mission

Journal ref: Springer Proc. Phys. 428, 57-64 (2025)

Modeling reflection spectra of super-Eddington X-ray sources

Authors: Swarnim Shashank, Askar B. Abdikamalov, Honghui Liu, Temurbek Mirzaev, Jiachen Jiang, Cosimo Bambi, Fergus Baker, Andrew Young

Abstract: Relativistic reflection is a common feature in the X-ray observations of accreting compact objects. We present reflux, a new X-ray reflection model for spectral analysis of super-Eddington sources. We develop two relativistic reflection frameworks for super-Eddington accretion: a slim-disk model that self-consistently accounts for disk thickening and self-shadowing, and an optically thick wind mod… ▽ More Relativistic reflection is a common feature in the X-ray observations of accreting compact objects. We present reflux, a new X-ray reflection model for spectral analysis of super-Eddington sources. We develop two relativistic reflection frameworks for super-Eddington accretion: a slim-disk model that self-consistently accounts for disk thickening and self-shadowing, and an optically thick wind model that treats reflection off a funnel-shaped outflow. The slim-disk model offers a geometry where the inner disk thickness is proportional to radius, becoming thicker as the mass accretion rate increases. The wind model measures the opening angle of the funnel, the wind speed, and wind acceleration radius. The slim-disk profile reduces the brightness of the blue horn in the Fe K emission line for a fixed emissivity and significantly changes the intensity profile for a lamppost geometry. The wind model shows a blue-shifted iron line due to high velocity outflows. Both models assume a spherically symmetric spacetime. We apply the wind model to the XMM-Newton spectrum of the tidal disruption event Swift J1644+57, where the Fe K profile is expected to be shaped by scattering in an outflowing funnel. We constrain the opening angle of the funnel and find a high velocity of the wind. △ Less

Submitted 12 December, 2025; v1 submitted 17 July, 2024; originally announced July 2024.

Comments: 10 pages, 7 figures, accepted for publication on ApJ

Journal ref: Astrophys.J. 996:51 (2026)

Non-Kerr Constraints using Binary Black Hole inspirals considering phase modifications up to 4 PN order

Authors: Debtroy Das, Swarnim Shashank, Cosimo Bambi

Abstract: The gravitational field around an astrophysical black hole (BH) is thought to be described by the Kerr spacetime, which is a solution of the Einstein equation. Signatures of binary black hole (BBH) coalescence in gravitational waves (GW) follow the Kerr spacetime as the theoretical foundation. Hence, any possible deviations from the Kerr spacetime around BHs serve as a test of the nature of gravit… ▽ More The gravitational field around an astrophysical black hole (BH) is thought to be described by the Kerr spacetime, which is a solution of the Einstein equation. Signatures of binary black hole (BBH) coalescence in gravitational waves (GW) follow the Kerr spacetime as the theoretical foundation. Hence, any possible deviations from the Kerr spacetime around BHs serve as a test of the nature of gravity in the strong-field regime and of the predictions of General Relativity. In our study, we perform a theory-agnostic test of the Kerr hypothesis using BBH inspirals from the third Gravitational-wave Transient Catalog (GWTC-3). Considering the Johannsen metric, we compute the leading-order deviation to the emitted GW in the frequency domain. Our results provide constraints on two deformation parameters ($α_{13}$ and $ε_3$) and demonstrate the degeneracy between these two non-Kerr parameters. △ Less

Submitted 6 June, 2024; originally announced June 2024.

Comments: 10 pages, 6 figures. Supplemental material (16 pages, 16 figures) available from the authors upon reasonable request

Journal ref: Eur. Phys. J. C (2024) 84:1237

X-ray spectra of black hole X-ray binaries with returning radiation

Authors: Temurbek Mirzaev, Cosimo Bambi, Askar B. Abdikamalov, Jiachen Jiang, Honghui Liu, Shafqat Riaz, Swarnim Shashank

Abstract: In the disk-corona model, the X-ray spectrum of a stellar-mass black hole in an X-ray binary is characterized by three components: a thermal component from a thin and cold accretion disk, a Comptonized component from a hot corona, and a reflection component produced by illumination of the cold disk by the hot corona. In this paper, we assume a lamppost corona and we improve previous calculations o… ▽ More In the disk-corona model, the X-ray spectrum of a stellar-mass black hole in an X-ray binary is characterized by three components: a thermal component from a thin and cold accretion disk, a Comptonized component from a hot corona, and a reflection component produced by illumination of the cold disk by the hot corona. In this paper, we assume a lamppost corona and we improve previous calculations of the X-ray spectrum of black hole X-ray binaries. The reflection spectrum is produced by the direct radiation from the corona as well as by the returning radiation of the thermal and reflection components and is calculated considering the actual spectrum illuminating the disk. If we turn the corona off, the reflection spectrum is completely generated by the returning radiation of the thermal component, as it may happen for some sources in soft spectral states. After choosing the radial density profile of the accretion disk, the ionization parameter is calculated self-consistently at any radial coordinate of the disk from the illuminating X-ray flux and the local electron density. We show the predictions of our model in different regimes and we discuss its current limitations as well as the next steps to improve it. △ Less

Submitted 26 November, 2024; v1 submitted 3 June, 2024; originally announced June 2024.

Comments: 10 pages, 6 figures. v2: refereed version

Journal ref: Astrophys.J. 976: 229 (2024)

Numerical parameterization of stationary axisymmetric black holes in a theory agnostic framework

Authors: Olzhas Mukazhanov, Rittick Roy, Temurbek Mirzaev, Cosimo Bambi

Abstract: The pursuit of a comprehensive theory of gravity has led to the exploration of various alternative models, necessitating a model-independent framework. The Konoplya-Rezzolla-Zhidenko (KRZ) parameterization offers a robust method for approximating stationary axisymmetric black hole spacetimes, characterized by a rapidly converging continued-fraction expansion. However, while analytical metrics bene… ▽ More The pursuit of a comprehensive theory of gravity has led to the exploration of various alternative models, necessitating a model-independent framework. The Konoplya-Rezzolla-Zhidenko (KRZ) parameterization offers a robust method for approximating stationary axisymmetric black hole spacetimes, characterized by a rapidly converging continued-fraction expansion. However, while analytical metrics benefit from this approach, numerical metrics derived from complex gravitational theories remain presenting computational challenges. Bridging this gap, we propose a method for a numerical KRZ parameterization, tested and demonstrated on pseudo-numerical Kerr and Kerr-Sen spacetimes. Our approach involves constructing numerical grids to represent metric coefficients and using the grids for fitting the parameters up to an arbitrary order. We analyze the accuracy of our method across different orders of approximation, considering deviations in the metric functions and shadow images. In both Kerr and Kerr-Sen cases, we observe rapid convergence of errors with increasing orders of continued fractions, albeit with variations influenced by spin and charge. Our results underscore the potential of the proposed algorithm for parameterizing numerical metrics, offering a pathway for further investigations across diverse gravity theories. △ Less

Submitted 10 June, 2024; v1 submitted 25 April, 2024; originally announced April 2024.

Comments: 9 pages, 9 figures, 2 tables, accepted for publication in PRD

Journal ref: Phys. Rev. D 110, 024060 (2024)

Towards more accurate synthetic reflection spectra: improving the calculations of returning radiation

Authors: Temurbek Mirzaev, Shafqat Riaz, Askar B. Abdikamalov, Cosimo Bambi, Thomas Dauser, Javier A. Garcia, Jiachen Jiang, Honghui Liu, Swarnim Shashank

Abstract: We present a new model to calculate reflection spectra of thin accretion disks in Kerr spacetimes. Our model includes the effect of returning radiation, which is the radiation that is emitted by the disk and returns to the disk because of the strong light bending near a black hole. The major improvement with respect to the existing models is that it calculates the reflection spectrum at every poin… ▽ More We present a new model to calculate reflection spectra of thin accretion disks in Kerr spacetimes. Our model includes the effect of returning radiation, which is the radiation that is emitted by the disk and returns to the disk because of the strong light bending near a black hole. The major improvement with respect to the existing models is that it calculates the reflection spectrum at every point on the disk by using the actual spectrum of the incident radiation. Assuming a lamppost coronal geometry, we simulate simultaneous observations of NICER and NuSTAR of bright Galactic black holes and we fit the simulated data with the latest version of RELXILL (modified to read the table of REFLIONX, which is the non-relativistic reflection model used in our calculations). We find that RELXILL with returning radiation cannot fit well the simulated data when the black hole spin parameter is very high and the coronal height and disk's ionization parameter are low, and some parameters can be significantly overestimated or underestimated. We can find better fits and recover the correct input parameters as the value of the black hole spin parameter decreases and the value of the coronal height increases. △ Less

Submitted 8 April, 2024; v1 submitted 10 January, 2024; originally announced January 2024.

Comments: 19 pages, 14 figures. v2: refereed version

Journal ref: Astrophys.J. 965: 66 (2024)

Testing General Relativity with black hole X-ray data

Authors: Cosimo Bambi

Abstract: The theory of General Relativity has successfully passed a large number of observational tests without requiring any adjustment from its original version proposed by Einstein in 1915. The past 8 years have seen significant advancements in the study of the strong-field regime, which can now be tested with gravitational waves, X-ray data, and black hole imaging. This is a compact and pedagogical rev… ▽ More The theory of General Relativity has successfully passed a large number of observational tests without requiring any adjustment from its original version proposed by Einstein in 1915. The past 8 years have seen significant advancements in the study of the strong-field regime, which can now be tested with gravitational waves, X-ray data, and black hole imaging. This is a compact and pedagogical review on the state-of-the-art of the tests of General Relativity with black hole X-ray data. △ Less

Submitted 10 December, 2023; originally announced December 2023.

Comments: 10 pages, 2 figures. Talk given at the "XXXV International Workshop on High Energy Physics - From Quarks to Galaxies: Elucidating Dark Sides" (Protvino, Russia, 28 November - 1 December 2023)

Journal ref: Physics of Particles and Nuclei 55, 1420-1425 (2024)

About the ability of agnostic X-ray tests of the Kerr Hypothesis to discover new physics

Authors: Shuaitongze Zhao, Shafqat Riaz, Cosimo Bambi

Abstract: In the past decade, we have seen an unprecedented progress in our ability of testing general relativity in the strong field regime with black hole observations. Most studies have focused on the so-called tests of the Kerr hypothesis: they have tried to verify whether the spacetime geometry around black holes is described by the Kerr solution as expected in general relativity. One can follow either… ▽ More In the past decade, we have seen an unprecedented progress in our ability of testing general relativity in the strong field regime with black hole observations. Most studies have focused on the so-called tests of the Kerr hypothesis: they have tried to verify whether the spacetime geometry around black holes is described by the Kerr solution as expected in general relativity. One can follow either a theory-specific analysis or an agnostic approach. Each strategy has its advantages and disadvantages. In this work, we study the ability of agnostic X-ray tests of the Kerr hypothesis to discover new physics. We simulate X-ray observations of bright Galactic black holes of specific theories of gravity and we analyze the simulated data with a reflection model employing the correct theory of gravity and another reflection model for agnostic tests of the Kerr hypothesis. Our results suggest that agnostic X-ray tests are valid tools to discover new physics, but their constraining power may be lower than a theory-specific analysis. △ Less

Submitted 19 March, 2024; v1 submitted 29 October, 2023; originally announced October 2023.

Comments: 12 pages, 5 figures. v2: refereed version

Journal ref: Phys. Rev. D 109, 064059 (2024)

Kerr-Taub-NUT spacetime to explain the jet power and the radiative efficiency of astrophysical black holes

Authors: Bakhtiyor Narzilloev, Ahmadjon Abdujabbarov, Bobomurat Ahmedov, Cosimo Bambi

Abstract: In this work, we investigate the electromagnetic energy released by astrophysical black holes within the Kerr-Taub-NUT solution, which describes rotating black holes with a nonvanishing gravitomagnetic charge. In our study, we consider the black holes in the X-ray binary systems GRS 1915+105, GRO J1655-40, XTE J1550-564, A0620-00, H1743-322, and GRS 1124-683. We show that the Kerr-Taub-NUT spaceti… ▽ More In this work, we investigate the electromagnetic energy released by astrophysical black holes within the Kerr-Taub-NUT solution, which describes rotating black holes with a nonvanishing gravitomagnetic charge. In our study, we consider the black holes in the X-ray binary systems GRS 1915+105, GRO J1655-40, XTE J1550-564, A0620-00, H1743-322, and GRS 1124-683. We show that the Kerr-Taub-NUT spacetime can explain the radiative efficiency of these sources inferred from the continuum fitting method (CFM). We also show that, in the framework of the Blandford-Znajeck mechanism, it is possible to reproduce the observed jet power. We unify the results of the two analyses for the selected objects to get more stringent constraints on the spacetime parameters. We show that, as in the case of the Kerr spacetime, the Kerr-Taub-NUT solution cannot simultaneously explain the observed jet power and radiative efficiency of GRS 1915+105. △ Less

Submitted 10 November, 2023; v1 submitted 16 October, 2023; originally announced October 2023.

Comments: 13 pages, 9 figures. v3: references added

Journal ref: Phys. Rev. D 108, 103013 (2023)

Regular Black Holes: Towards a New Paradigm of Gravitational Collapse

Authors: Cosimo Bambi

Abstract: Black holes are one of the most fascinating predictions of general relativity. They are the natural product of the complete gravitational collapse of matter and today we have a body of observational evidence supporting the existence of black holes in the Universe. However, general relativity predicts that at the center of black holes there are spacetime singularities, where predictability is lost… ▽ More Black holes are one of the most fascinating predictions of general relativity. They are the natural product of the complete gravitational collapse of matter and today we have a body of observational evidence supporting the existence of black holes in the Universe. However, general relativity predicts that at the center of black holes there are spacetime singularities, where predictability is lost and standard physics breaks down. It is widely believed that spacetime singularities are a symptom of the limitations of general relativity and must be solved within a theory of quantum gravity. Since we do not have yet any mature and reliable candidate for a quantum gravity theory, researchers have studied toy-models of singularity-free black holes and of singularity-free gravitational collapses in order to explore possible implications of the yet unknown theory of quantum gravity. This book reviews all main models of regular black holes and non-singular gravitational collapses proposed in the literature, and discuss the theoretical and observational implications of these scenarios. △ Less

Submitted 25 July, 2023; originally announced July 2023.

Comments: 4 pages, no figures. Preface and table of contents of the book "Regular Black Holes: Towards a New Paradigm of Gravitational Collapse" (Springer Singapore, 2023). ISBN: 978-981-99-1595-8 (Hardcover), 978-981-99-1596-5 (eBook)

Testing General Relativity with Black Hole X-Ray Data and ABHModels

Authors: Cosimo Bambi, Askar B. Abdikamalov, Honghui Liu, Shafqat Riaz, Swarnim Shashank, Menglei Zhou

Abstract: The past 10 years have seen tremendous progress in our capability of testing General Relativity in the strong field regime with black hole observations. 10 years ago, the theory of General Relativity was almost completely unexplored in the strong field regime. Today, we have gravitational wave data of the coalescence of stellar-mass black holes, radio images of the supermassive black holes SgrA… ▽ More The past 10 years have seen tremendous progress in our capability of testing General Relativity in the strong field regime with black hole observations. 10 years ago, the theory of General Relativity was almost completely unexplored in the strong field regime. Today, we have gravitational wave data of the coalescence of stellar-mass black holes, radio images of the supermassive black holes SgrA$^*$ and M87$^*$, and high-quality X-ray data of stellar-mass black holes in X-ray binaries and supermassive black holes in active galactic nuclei. In this manuscript, we will review current efforts to test General Relativity with black hole X-ray data and we will provide a detailed description of the public codes available on ABHModels. △ Less

Submitted 23 April, 2024; v1 submitted 24 July, 2023; originally announced July 2023.

Comments: 31 pages, 5 figures. Talk given at the Frascati Workshop 2023 "Multifrequency Behaviour of High Energy Cosmic Sources - XIV" (Palermo, Italy, 12-17 June 2023). v2: refereed version

Journal ref: PoS MULTIF2023, 016 (2024)

Testing Regular Black Holes with X-ray data of GX 339-4

Authors: Shafqat Riaz, Michail Kyriazis, Askar B. Abdikamalov, Cosimo Bambi, Swarnim Shashank

Abstract: Regular black holes are singularity-free black hole spacetimes proposed to solve the problem of the presence of spacetime singularities that plagues the black holes of general relativity and most theories of gravity. In this work, we consider the regular black holes recently proposed by Mazza, Franzin & Liberati and we extend previous studies to get a more stringent observational constraint on the… ▽ More Regular black holes are singularity-free black hole spacetimes proposed to solve the problem of the presence of spacetime singularities that plagues the black holes of general relativity and most theories of gravity. In this work, we consider the regular black holes recently proposed by Mazza, Franzin & Liberati and we extend previous studies to get a more stringent observational constraint on the regularization parameter $l$. We study simultaneous observations of NuSTAR and Swift of the Galactic black hole in GX 339-4 during its outburst in 2015. The quality of the NuSTAR data is exceptionally good and the spectrum of the source presents both a strong thermal component and prominent relativistically blurred reflection features. This permits us to measure the regularization parameter $l$ from the simultaneous analysis of the thermal spectrum and the reflection features. From our analysis, we find the constraint $l/M < 0.44$ (90% CL), which is stronger than previous constraints inferred with X-ray and gravitational wave data. △ Less

Submitted 12 March, 2025; v1 submitted 16 June, 2023; originally announced June 2023.

Comments: 1+20 pages, 4 figures. v2: refereed version

Journal ref: JCAP 2503:022 (2025)

X-Ray Tests of General Relativity with Black Holes

Authors: Cosimo Bambi

Abstract: General relativity is one of the pillars of modern physics. For decades, the theory has been mainly tested in the weak field regime with experiments in the Solar System and radio observations of binary pulsars. Until 2015, the strong field regime was almost completely unexplored. Thanks to new observational facilities, the situation has dramatically changed in the last few years. Today we have gra… ▽ More General relativity is one of the pillars of modern physics. For decades, the theory has been mainly tested in the weak field regime with experiments in the Solar System and radio observations of binary pulsars. Until 2015, the strong field regime was almost completely unexplored. Thanks to new observational facilities, the situation has dramatically changed in the last few years. Today we have gravitational wave data of the coalesce of stellar-mass compact objects from the LIGO-Virgo-KAGRA Collaboration, images at mm wavelengths of the supermassive black holes in M87$^*$ and SgrA$^*$ from the Event Horizon Telescope Collaboration, and X-ray data of accreting compact objects from a number of X-ray missions. Gravitational wave tests and black hole imaging tests are certainly more popular and are discussed in other articles of this Special Issue. The aim of the present manuscript is to provide a pedagogical review on X-ray tests of general relativity with black holes and to compare this kind of tests with those possible with gravitational wave data and black hole imaging. △ Less

Submitted 18 June, 2023; v1 submitted 18 May, 2023; originally announced May 2023.

Comments: 16 pages, 5 figures. Invited contribution for the Special Issue "Role of Black Holes in Testing Modified Theories of Gravity" for Symmetry (Ed. Rahul Kumar Walia). v2: refereed version

Journal ref: Symmetry 15: 1277 (2023)

Impact of the returning radiation in current tests of the Kerr black hole hypothesis using X-ray reflection spectroscopy

Authors: Shafqat Riaz, Temurbek Mirzaev, Askar B. Abdikamalov, Cosimo Bambi

Abstract: The past 10 years have seen remarkable progress in our capability of analyzing reflection features in the X-ray spectra of accreting black holes. Today X-ray reflection spectroscopy is a mature technique and a powerful tool for studying the accretion process around black holes, measuring black hole spins, and testing Einstein's theory of General Relativity in the strong field regime. However, curr… ▽ More The past 10 years have seen remarkable progress in our capability of analyzing reflection features in the X-ray spectra of accreting black holes. Today X-ray reflection spectroscopy is a mature technique and a powerful tool for studying the accretion process around black holes, measuring black hole spins, and testing Einstein's theory of General Relativity in the strong field regime. However, current reflection models still rely on a number of simplifications and caution is necessary when we derive very precise measurements. In this paper, we study the impact of the returning radiation on our capability of measuring the properties of black holes using X-ray reflection spectroscopy, and in particular on our capability of testing the Kerr black hole hypothesis. While the returning radiation alters the reflection spectrum of the disk, from the analysis of our simulations we find that models without returning radiation can normally recover well the correct black hole spin parameters and can test the Kerr metric. Our study thus confirms that current tests of the Kerr hypothesis using X-ray reflection spectroscopy can be robust. △ Less

Submitted 22 September, 2023; v1 submitted 22 March, 2023; originally announced March 2023.

Comments: 12 pages, 10 figures. v2: refereed version

Journal ref: Eur. Phys. J. C (2023) 83:838

Testing the $δ$-Kerr metric with black hole X-ray data

Authors: Jiahao Tao, Shafqat Riaz, Biao Zhou, Askar B. Abdikamalov, Cosimo Bambi, Daniele Malafarina

Abstract: The spacetime around astrophysical black holes is thought to be described by the Kerr solution. However, even within general relativity, there is not yet a proof that the final product of the complete collapse of an uncharged body can only be a Kerr black hole. We can thus speculate on the possibility that the spacetime around astrophysical black holes may be described by other solutions of the Ei… ▽ More The spacetime around astrophysical black holes is thought to be described by the Kerr solution. However, even within general relativity, there is not yet a proof that the final product of the complete collapse of an uncharged body can only be a Kerr black hole. We can thus speculate on the possibility that the spacetime around astrophysical black holes may be described by other solutions of the Einstein Equations and we can test such a hypothesis with observations. In this work, we consider the $δ$-Kerr metric, which is an exact solution of the field equations in vacuum and can be obtained from a non-linear superposition of the Kerr metric with a static axially symmetric solution, often referred to as the $δ$-metric. The parameter $δ=1+q$ quantifies the departure of the source from the Kerr metric and for $q=0$ we recover the Kerr solution. From the analysis of the reflection features in the X-ray spectrum of the Galactic black hole in EXO 1846-031, we find $-0.1 < q < 0.7$ (90% CL), which is consistent with the hypothesis that the spacetime around the compact object in EXO 1846-031 is a Kerr black hole but does not entirely rule out the $δ$-Kerr metric. △ Less

Submitted 25 October, 2023; v1 submitted 28 January, 2023; originally announced January 2023.

Comments: 17 pages, 7 figures. v2: refereed version

Journal ref: Phys. Rev. D 108, 083036 (2023)

Search for Variations of Fundamental Constants

Authors: Cosimo Bambi

Abstract: The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the fundamental theory and their value is instead determined, for example, by the background value of some new field or the size of extra dimensions. So far, most studies h… ▽ More The possibility of variations of the values of fundamental constants is a phenomenon predicted by a number of scenarios beyond General Relativity. This can happen if ``our'' fundamental constants are not the actual constants of the fundamental theory and their value is instead determined, for example, by the background value of some new field or the size of extra dimensions. So far, most studies have been devoted to constrain possible temporal variations of the electromagnetic fine structure constant $α$, the proton to electron mass ratio $μ= m_p/m_e$, and the gravitational constant $G_{\rm N}$. Apart some claims of the detection of a temporal or spatial variation of $α$ and $μ$, so far there is no clear observational evidence of any variation of our fundamental constants. △ Less

Submitted 21 October, 2022; originally announced October 2022.

Comments: 15 pages, no figures. Chapter for the book "Recent Progress on Gravity Tests" (Eds. C. Bambi and A. Cárdenas-Avendaño, Springer Singapore, expected in 2023)

Testing Gravity with Black Hole X-Ray Data

Authors: Cosimo Bambi

Abstract: The analysis of the properties of the X-ray radiation emitted from geometrically thin accretion disks around black holes can be a powerful tool to test General Relativity in the strong field regime. This chapter reviews the state-of-the-art of gravity tests with black hole X-ray data. So far, most efforts have been devoted to test the Kerr hypothesis - namely that the spacetime around astrophysica… ▽ More The analysis of the properties of the X-ray radiation emitted from geometrically thin accretion disks around black holes can be a powerful tool to test General Relativity in the strong field regime. This chapter reviews the state-of-the-art of gravity tests with black hole X-ray data. So far, most efforts have been devoted to test the Kerr hypothesis - namely that the spacetime around astrophysical black holes is described by the Kerr solution - and X-ray data can currently provide among the most stringent constraints on possible deviations from the Kerr geometry. As of now, all X-ray analyses are consistent with the predictions of General Relativity. △ Less

Submitted 11 October, 2022; originally announced October 2022.

Comments: 35 pages, 13 figures. Chapter for the book "Recent Progress on Gravity Tests" (Eds. C. Bambi and A. Cárdenas-Avendaño, Springer Singapore, expected in 2023). It reviews current X-ray constraints on the Kerr hypothesis and discusses the systematic uncertainties

Testing relativistic reflection models with GRMHD simulations of accreting black holes

Authors: Swarnim Shashank, Shafqat Riaz, Askar B. Abdikamalov, Cosimo Bambi

Abstract: X-ray reflection spectroscopy is currently one of the leading techniques for studying the inner part of accretion disks around black holes, measuring black hole spins, and even testing fundamental physics in strong gravitational fields. However, the accuracy of these measurements depends on the reflection models employed for the spectral analysis, which are sometimes questioned. In this work, we u… ▽ More X-ray reflection spectroscopy is currently one of the leading techniques for studying the inner part of accretion disks around black holes, measuring black hole spins, and even testing fundamental physics in strong gravitational fields. However, the accuracy of these measurements depends on the reflection models employed for the spectral analysis, which are sometimes questioned. In this work, we use a general relativistic magnetohydrodynamic (GRMHD) code to generate a thin accretion disk in Kerr spacetime and ray-tracing techniques to calculate its relativistically broadened reflection spectrum. We simulate NuSTAR observations and we test the capability of current reflection models based on Novikov-Thorne disks to recover the correct input parameters. Our study shows that we can measure the correct input parameters in the case of high inclination angle sources, while we find some minor discrepancy when the inclination angle of the disk is low. △ Less

Submitted 13 October, 2022; v1 submitted 23 July, 2022; originally announced July 2022.

Comments: 10 pages, 10 figures. v2: refereed version

Journal ref: Astrophys.J. 938: 53 (2022)

Probing bumblebee gravity with black hole X-ray data

Authors: Jiale Gu, Shafqat Riaz, Askar B. Abdikamalov, Dimitry Ayzenberg, Cosimo Bambi

Abstract: Bumblebee gravity is one of the simplest gravity theories with spontaneous Lorentz symmetry breaking. Since we know a rotating black hole solution in bumblebee gravity, we can potentially test this model with the available astrophysical observations of black holes. In this work, we construct a reflection model in bumblebee gravity and we use our model to analyze the reflection features of a NuSTAR… ▽ More Bumblebee gravity is one of the simplest gravity theories with spontaneous Lorentz symmetry breaking. Since we know a rotating black hole solution in bumblebee gravity, we can potentially test this model with the available astrophysical observations of black holes. In this work, we construct a reflection model in bumblebee gravity and we use our model to analyze the reflection features of a NuSTAR spectrum of the Galactic black hole EXO 1846-031 in order to constrain the Lorentz-violating parameter $\ell$. We find that the analysis of the reflection features in the spectrum of EXO 1846-031 cannot constrain the parameter $\ell$ because of a very strong degeneracy between the estimates of $\ell$ and of the black hole spin parameter $a_*$. Such a degeneracy may be broken by combining other observations. △ Less

Submitted 15 August, 2022; v1 submitted 29 June, 2022; originally announced June 2022.

Comments: 9 pages, 5 figures. v2: refereed version

Journal ref: Eur. Phys. J. C (2022) 82:708

Testing regular black holes with X-ray and GW data

Authors: Shafqat Riaz, Swarnim Shashank, Rittick Roy, Askar B. Abdikamalov, Dimitry Ayzenberg, Cosimo Bambi, Zuobin Zhang, Menglei Zhou

Abstract: The presence of spacetime singularities in physically relevant solutions of the Einstein Equations is normally interpreted as a symptom of the breakdown of classical general relativity at very high densities/curvatures. However, despite significant efforts in the past decades, we do not have yet any robust theoretical framework to solve the problem of spacetime singularities. In this context, the… ▽ More The presence of spacetime singularities in physically relevant solutions of the Einstein Equations is normally interpreted as a symptom of the breakdown of classical general relativity at very high densities/curvatures. However, despite significant efforts in the past decades, we do not have yet any robust theoretical framework to solve the problem of spacetime singularities. In this context, the past few years have seen an increasing interest in the study of phenomenological scenarios to describe singularity-free black holes, gravitational collapses, and cosmological models. In the present work, we consider the recent proposal by Mazza, Franzin & Liberati for a rotating regular black hole and we measure their regularization parameter $l$ from the available X-ray and gravitational wave black hole data. For $l = 0$, we recover the singular Kerr solution of general relativity, while for $l \neq 0$ we can have a regular black hole or a regular wormhole. Our analysis shows that the available data are consistent with a vanishing regularization parameter $l$ and we can constrain its value. From a NuSTAR spectrum of the Galactic black hole in EXO 1846-031, we find $l/M < 0.49$ (90% CL). From the gravitational wave event GW190707A, we find $l/M < 0.72$ (90% CL). △ Less

Submitted 5 November, 2022; v1 submitted 8 June, 2022; originally announced June 2022.

Comments: 31 pages, 10 figures. v3: refereed version. v4: clarified a couple of passages

Journal ref: JCAP 2210:040 (2022)

Horizon-scale tests of gravity theories and fundamental physics from the Event Horizon Telescope image of Sagittarius A$^*$

Authors: Sunny Vagnozzi, Rittick Roy, Yu-Dai Tsai, Luca Visinelli, Misba Afrin, Alireza Allahyari, Parth Bambhaniya, Dipanjan Dey, Sushant G. Ghosh, Pankaj S. Joshi, Kimet Jusufi, Mohsen Khodadi, Rahul Kumar Walia, Ali Övgün, Cosimo Bambi

Abstract: Horizon-scale images of black holes (BHs) and their shadows have opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. We consider a wide range of well-motivated deviations from classical General Relativity (GR) BH solutions, and constrain them using the Event Horizon Telescope (EHT) observations of Sagittarius A$^*$ (Sgr A$^*$), connecting the si… ▽ More Horizon-scale images of black holes (BHs) and their shadows have opened an unprecedented window onto tests of gravity and fundamental physics in the strong-field regime. We consider a wide range of well-motivated deviations from classical General Relativity (GR) BH solutions, and constrain them using the Event Horizon Telescope (EHT) observations of Sagittarius A$^*$ (Sgr A$^*$), connecting the size of the bright ring of emission to that of the underlying BH shadow and exploiting high-precision measurements of Sgr A$^*$'s mass-to-distance ratio. The scenarios we consider, and whose fundamental parameters we constrain, include various regular BHs, string-inspired space-times, violations of the no-hair theorem driven by additional fields, alternative theories of gravity, novel fundamental physics frameworks, and BH mimickers including well-motivated wormhole and naked singularity space-times. We demonstrate that the EHT image of Sgr A$^*$ places particularly stringent constraints on models predicting a shadow size larger than that of a Schwarzschild BH of a given mass, with the resulting limits in some cases surpassing cosmological ones. Our results are among the first tests of fundamental physics from the shadow of Sgr A$^*$ and, while the latter appears to be in excellent agreement with the predictions of GR, we have shown that a number of well motivated alternative scenarios, including BH mimickers, are far from being ruled out at present. △ Less

Submitted 26 May, 2023; v1 submitted 16 May, 2022; originally announced May 2022.

Comments: 82 pages, 47 figures, 50+ models tested. v3: fixed a few figures, clarified several points, included various analytical expressions for shadow sizes within the different models, added a few references, included a summary table (Table II). Version accepted for publication in Classical and Quantum Gravity

Journal ref: Class. Quant. Grav. 40 (2023) 165007

Observational appearance of Kaluza-Klein black holes

Authors: Temurbek Mirzaev, Askar B. Abdikamalov, Ahmadjon A. Abdujabbarov, Dimitry Ayzenberg, Bobomurat Ahmedov, Cosimo Bambi

Abstract: The optical properties of rotating black holes in Kaluza-Klein theory described by the total mass, spin, and electric and magnetic charges are investigated in detail. Using a developed general relativistic ray-tracing code to calculate the motion of photons, the numerous shadows of Kaluza-Klein black holes are generated. The properties of the black hole shadow and the light deflection angle around… ▽ More The optical properties of rotating black holes in Kaluza-Klein theory described by the total mass, spin, and electric and magnetic charges are investigated in detail. Using a developed general relativistic ray-tracing code to calculate the motion of photons, the numerous shadows of Kaluza-Klein black holes are generated. The properties of the black hole shadow and the light deflection angle around these black holes are also studied in order to put constraints on the parameters of Kaluza-Klein black holes using M87* shadow observations. The possibility of imposing constraints on Kaluza-Klein black holes using shadow observations is investigated. Moreover, we find that small charges (electric and magnetic) of the black hole can meet these constraints. We conclude that with the current precision of the M87* black hole shadow image observation by the EHT collaboration, the shadow observations of Kaluza-Klein black holes are indistinguishable from that of the Kerr black hole. Much better observational accuracy than the current capabilities of the EHT collaboration are required in order to place verified constraints on the parameters of modified theories of gravity in the strong field regime. △ Less

Submitted 10 September, 2023; v1 submitted 4 February, 2022; originally announced February 2022.

Comments: 13 pages, 9 figures. v2: refereed version

Journal ref: Eur. Phys. J. C (2023) 83:800

Constraining the Konoplya-Rezzolla-Zhidenko deformation parameters III: limits from stellar-mass black holes using gravitational-wave observations

Authors: Swarnim Shashank, Cosimo Bambi

Abstract: Gravitational-wave observations of binary black holes provide a suitable arena to test the fundamental nature of gravity in the strong-field regime. Using the data of the inspiral of 29 events detected by the LIGO-Virgo observatories, we perform a theory-agnostic test of the Kerr hypothesis. We compute the leading-order deviation to the gravitational waves emitted in the frequency domain and provi… ▽ More Gravitational-wave observations of binary black holes provide a suitable arena to test the fundamental nature of gravity in the strong-field regime. Using the data of the inspiral of 29 events detected by the LIGO-Virgo observatories, we perform a theory-agnostic test of the Kerr hypothesis. We compute the leading-order deviation to the gravitational waves emitted in the frequency domain and provide constraints on two deformation parameters ($δ_1$ and $δ_2$) belonging to a general class of axisymmetric non-Kerr black hole spacetimes proposed by Konoplya, Rezzolla & Zhidenko. Our study shows that all the analyzed events are consistent with the Kerr hypothesis. The LIGO-Virgo data provide stronger constraints on $δ_1$ and $δ_2$ than those obtained in our previous studies with X-ray data (Papers I and II), while, on the other hand, they cannot constrain the other deformation parameters of the Konoplya-Rezzolla-Zhidenko metric ($δ_3$, $δ_4$, $δ_5$, and $δ_6$). △ Less

Submitted 4 May, 2022; v1 submitted 10 December, 2021; originally announced December 2021.

Comments: 11 pages, 2 figures. v2: refereed version

Journal ref: Phys. Rev. D 105, 104004 (2022)

Tests of General Relativity using black hole X-ray data

Authors: Dimitry Ayzenberg, Cosimo Bambi

Abstract: The theory of General Relativity has successfully passed a large number of observational tests. The theory has been extensively tested in the weak-field regime with experiments in the Solar System and observations of binary pulsars. Recently, there have seen significant advancements in the study of the strong-field regime, which can now be tested with gravitational waves, X-ray data, and mm Very L… ▽ More The theory of General Relativity has successfully passed a large number of observational tests. The theory has been extensively tested in the weak-field regime with experiments in the Solar System and observations of binary pulsars. Recently, there have seen significant advancements in the study of the strong-field regime, which can now be tested with gravitational waves, X-ray data, and mm Very Long Baseline Interferometry observations. Here we summarize the state-of-the-art of the tests of General Relativity with black hole X-ray data, discussing its recent progress and future developments. △ Less

Submitted 27 November, 2021; originally announced November 2021.

Comments: 37 pages, 8 figures. Invited chapter for the "Handbook of X-ray and Gamma-ray Astrophysics" (Eds. C. Bambi and A. Santangelo, Springer Singapore, expected in 2022)

The spins of the Galactic black holes in MAXI J1535-571 and 4U 1630-472 from Insight-HXMT

Authors: Qichun Liu, Honghui Liu, Cosimo Bambi, Long Ji

Abstract: Insight-HXMT is the first Chinese X-ray astronomical mission. With a 1-250 keV bandpass, an energy resolution of 150 eV at 6 keV, and without being subject to pile-up distortions, it is suitable to study bright X-ray sources like Galactic black holes. In the present paper, we study Insight-HXMT observations of the X-ray binaries MAXI J1535-571 and 4U 1630-472 during their outbursts in 2017 and 202… ▽ More Insight-HXMT is the first Chinese X-ray astronomical mission. With a 1-250 keV bandpass, an energy resolution of 150 eV at 6 keV, and without being subject to pile-up distortions, it is suitable to study bright X-ray sources like Galactic black holes. In the present paper, we study Insight-HXMT observations of the X-ray binaries MAXI J1535-571 and 4U 1630-472 during their outbursts in 2017 and 2020, respectively. From the analysis of the reflection features, we are able to infer the black hole spin parameter in the two sources. For MAXI J1535-571, we find a spin parameter very close to 1, $a_* = 0.9916 \pm 0.0012$ (90% C.L., statistical error), which is consistent with the previous NuSTAR measurement. For 4U 1630-472, we find a moderately high value of the black hole spin parameter, $a_* =0.817 \pm 0.014$ (90% C.L., statistical error), which is lower than the almost extremal value found with NuSTAR data. △ Less

Submitted 19 March, 2022; v1 submitted 1 November, 2021; originally announced November 2021.

Comments: 11 pages, 8 figures. v2: refereed version. v3: changed layout and fixed the size of Tab. 4

Journal ref: Mon. Not. Roy. Astron. Soc. 512, 2082-2092 (2022)

Dynamics and Fundamental Frequencies of Test Particles Orbiting Kerr-Newman-NUT-Kiselev Blacks Hole in Rastall Gravity

Authors: Bakhtiyor Narzilloev, Ibrar Hussain, Ahmadjon Abdujabbarov, Bobomurat Ahmedov, Cosimo Bambi

Abstract: The spacetime properties in the exterior of the Kerr-Newman-NUT-Kiselev black hole in the Rastall theory of gravity, through particle dynamics are investigated with the aim to find possible degeneracy of the different black hole parameters. We show that the effective potential, the energy, and the angular momentum of a test particle moving in the spacetime of such a black hole strongly depend on t… ▽ More The spacetime properties in the exterior of the Kerr-Newman-NUT-Kiselev black hole in the Rastall theory of gravity, through particle dynamics are investigated with the aim to find possible degeneracy of the different black hole parameters. We show that the effective potential, the energy, and the angular momentum of a test particle moving in the spacetime of such a black hole strongly depend on the central black hole parameters. We also evaluate the innermost stable circular orbit radii of test particles and show how the spacetime parameters can act on them. Further, we show the results for the fundamental frequencies of test particles moving at small distances from the circular orbits in the equatorial plane. We demonstrate that change in the Rastall parameter $κλ$, can make the radial epicyclic frequency to become zero at larger distances from the central source. We also notice that for the vertical epicyclic frequencies, in the case of the Kerr-Newman-NUT-Kiselev black hole in the Rastall theory of gravity lower frequencies are observed as compared to the frequencies observed in the case of the Kerr black hole. Finally, we show that for the Kerr-Newman-NUT-Kiselev black hole in the Rastall gravity, the Keplerian frequencies are almost identical with the frequencies noticed in the case of the Kerr black hole and the difference between the two can only be observed in the regions in a very close vicinity to the central black hole, studied in the present work. △ Less

Submitted 4 October, 2021; originally announced October 2021.

Comments: 14 pages, 7 figures. Accepted for publication in EPJ Plus

Journal ref: Eur. Phys. J. Plus (2021) 136:1032

Motion of Particles and Gravitational Lensing Around (2+1)-dimensional BTZ black holes in Gauss-Bonnet Gravity

Authors: Bakhtiyor Narzilloev, Sanjar Shaymatov, Ibrar Hussain, Ahmadjon Abdujabbarov, Bobomurat Ahmedov, Cosimo Bambi

Abstract: We study motion of test particles and photons in the vicinity of (2+1) dimensional Gauss-Bonnet (GB) BTZ black hole. We find that the presence of the coupling constant serves as an attractive gravitational charge, shifting the innermost stable circular orbits outward with respect to the one for this theory in 4 dimensions. Further we consider the gravitational lensing, to test the GB gravity in (2… ▽ More We study motion of test particles and photons in the vicinity of (2+1) dimensional Gauss-Bonnet (GB) BTZ black hole. We find that the presence of the coupling constant serves as an attractive gravitational charge, shifting the innermost stable circular orbits outward with respect to the one for this theory in 4 dimensions. Further we consider the gravitational lensing, to test the GB gravity in (2+1) dimensions and show that the presence of GB parameter causes the bending angle to grow up first with the increase of the inverse of closest approach distance, $u_0$, then have its maximum value for specific $u_0^*$, and then reduce until zero. We also show that increase in the value of the GB parameter makes the bending angle smaller and the increase in the absolute value of the negative cosmological constant produces opposite effect on this angle. △ Less

Submitted 6 September, 2021; originally announced September 2021.

Comments: 11 pages, 6 figures. Accepted for publication in EPJC

Journal ref: Eur. Phys. J. C (2021) 81:849

A reflection model with a radial disk density profile

Authors: Askar B. Abdikamalov, Dimitry Ayzenberg, Cosimo Bambi, Honghui Liu, Ashutosh Tripathi

Abstract: In this paper we present RELXILLDGRAD_NK, a relativistic reflection model in which the electron density of the accretion disk is allowed to have a radial power-law profile. The ionization parameter has also a non-constant radial profile and is calculated self-consistently from the electron density and the emissivity. We show the impact of the implementation of the electron density gradient in our… ▽ More In this paper we present RELXILLDGRAD_NK, a relativistic reflection model in which the electron density of the accretion disk is allowed to have a radial power-law profile. The ionization parameter has also a non-constant radial profile and is calculated self-consistently from the electron density and the emissivity. We show the impact of the implementation of the electron density gradient in our model by analyzing a NuSTAR spectrum of the Galactic black hole in EXO 1846-031 during its last outburst in 2019 and a putative future observation of the same source with Athena and eXTP. For the NuSTAR spectrum, we find that the new model provides a better fit, but there is no significant difference in the estimation of the model parameters. For the Athena+eXTP simulation, we find that a model without a disk density profile is unsuitable to test the spacetime metric around the compact object, in the sense that modeling uncertainties can incorrectly lead to finding a non-vanishing deformation from the Kerr solution. △ Less

Submitted 21 December, 2021; v1 submitted 1 August, 2021; originally announced August 2021.

Comments: 11 pages, 9 figures. v2: refereed version

Journal ref: Astrophys.J. 923: 175 (2021)

Constraining the Konoplya-Rezzolla-Zhidenko deformation parameters II: limits from stellar-mass black hole X-ray data

Authors: Zhibo Yu, Qunfeng Jiang, Askar B. Abdikamalov, Dimitry Ayzenberg, Cosimo Bambi, Honghui Liu, Sourabh Nampalliwar, Ashutosh Tripathi

Abstract: Astrophysical black holes are thought to be the Kerr black holes predicted by general relativity, but macroscopic deviations from the Kerr solution can be expected from a number of scenarios involving new physics. In Paper I, we studied the reflection features in NuSTAR and XMM-Newton spectra of the supermassive black hole at the center of the galaxy MCG-06-30-15 and we constrained a set of deform… ▽ More Astrophysical black holes are thought to be the Kerr black holes predicted by general relativity, but macroscopic deviations from the Kerr solution can be expected from a number of scenarios involving new physics. In Paper I, we studied the reflection features in NuSTAR and XMM-Newton spectra of the supermassive black hole at the center of the galaxy MCG-06-30-15 and we constrained a set of deformation parameters proposed by Konoplya, Rezzolla & Zhidenko (Phys. Rev. D93, 064015, 2016). In the present work, we analyze the X-ray data of a stellar-mass black hole within the same theoretical framework in order to probe a different curvature regime. We consider a NuSTAR observation of the X-ray binary EXO 1846-031 during its outburst in 2019. As in the case of Paper I, all our fits are consistent with the Kerr black hole hypothesis, but some deformation parameters cannot be constrained well. △ Less

Submitted 4 October, 2021; v1 submitted 22 June, 2021; originally announced June 2021.

Comments: 8 pages, 3 figures. v2: refereed version

Journal ref: Phys. Rev. D 104, 084035 (2021)

Testing the Kerr black hole hypothesis with the continuum-fitting and the iron line methods: the case of GRS 1915+105

Authors: Ashutosh Tripathi, Askar B. Abdikamalov, Dimitry Ayzenberg, Cosimo Bambi, Victoria Grinberg, Honghui Liu, Menglei Zhou

Abstract: The continuum-fitting and the iron line methods are currently the two leading techniques for probing the strong gravity region around accreting black holes. In the present work, we test the Kerr black hole hypothesis with the stellar-mass black hole in GRS 1915+105 by analyzing five disk-dominated RXTE spectra and one reflection-dominated Suzaku spectrum. The combination of the constraints from th… ▽ More The continuum-fitting and the iron line methods are currently the two leading techniques for probing the strong gravity region around accreting black holes. In the present work, we test the Kerr black hole hypothesis with the stellar-mass black hole in GRS 1915+105 by analyzing five disk-dominated RXTE spectra and one reflection-dominated Suzaku spectrum. The combination of the constraints from the continuum-fitting and the iron line methods has the potential to provide more stringent tests of the Kerr metric. Our constraint on the Johannsen deformation parameter $α_{13}$ is $-0.15 < α_{13} < 0.14$ at 3$σ$, where the Kerr metric is recovered when $α_{13} = 0$. △ Less

Submitted 11 January, 2022; v1 submitted 21 June, 2021; originally announced June 2021.

Comments: 12 pages, 8 figures. v2: refereed version

Journal ref: JCAP 2201:019 (2022)