Showing 1–50 of 103 results for author: Emparan, R

General Effective Theories of Black Holes in the Large D Limit

Authors: Roberto Emparan, Jordi Rafecas-Ventosa, Benson Way

Abstract: We derive the general form of the effective equations governing black hole dynamics in the limit of a large number of dimensions $D$. These split into a universal \emph{soap-bubble} embedding condition for stationary configurations and a set of nonlinear dynamical evolution equations describing near-horizon fluctuations of $O(1/D)$ amplitude over horizon scales of $O(1/\sqrt{D})$. We obtain these… ▽ More We derive the general form of the effective equations governing black hole dynamics in the limit of a large number of dimensions $D$. These split into a universal \emph{soap-bubble} embedding condition for stationary configurations and a set of nonlinear dynamical evolution equations describing near-horizon fluctuations of $O(1/D)$ amplitude over horizon scales of $O(1/\sqrt{D})$. We obtain these equations in full generality, including arbitrary asymptotic sources in the near-horizon region, and we show that they form a parabolic system with a well-posed initial value problem. To connect the various approaches to large-$D$ black hole dynamics, we also show that both the embedding and dynamical equations can be derived from the covariant membrane formalism. We clarify the intrinsic scope of the large-$D$ approach, emphasizing that it yields a well-posed dynamical evolution only on horizon scales of $O(1/\sqrt{D})$, which is the range where the most relevant horizon dynamics occur. Our results highlight the versatility of these effective theories for studying a wide class of black hole phenomena. △ Less

Submitted 6 January, 2026; v1 submitted 16 December, 2025; originally announced December 2025.

Comments: 38 pages, 2 figures. v2: Improved discussion of symmetries and gauge dependence. 41 pages

Novel black saddles for 5d gravitational indices and the index enigma

Authors: Jan Boruch, Roberto Emparan, Luca V. Iliesiu, Sameer Murthy

Abstract: We construct a series of novel Euclidean multi-black-hole, black ring, black Saturn, and black lens solutions to $5d$ supergravity that contribute as saddle-points to the $5d$ gravitational supersymmetric index, either in asymptotically flat space or in asymptotically AdS$_3\times S^2$. All these solutions are supersymmetric, have finite temperature, and an appropriate angular velocity turned on t… ▽ More We construct a series of novel Euclidean multi-black-hole, black ring, black Saturn, and black lens solutions to $5d$ supergravity that contribute as saddle-points to the $5d$ gravitational supersymmetric index, either in asymptotically flat space or in asymptotically AdS$_3\times S^2$. All these solutions are supersymmetric, have finite temperature, and an appropriate angular velocity turned on that makes fermionic fields periodic around the thermal circle. They contribute either to the helicity supertrace of supergravity in $5d$ flat space or to the elliptic genus of a supergravity theory in AdS$_3 \times S^2$. Their on-shell actions are independent of temperature, as consistent with the computation of a protected index, and equal to the entropy of the corresponding extremal black object. Our construction relies on uplifting saddles that can be singular in $4d$, but which are desingularized in $5d$. The resulting saddles exhibit a novel ``index enigma'', not encountered in previous Lorentzian solutions. One example of this enigma is that, in the computation of the index in asymptotically flat space, less symmetric black ring saddles dominate over the contributions from $5d$ black holes. △ Less

Submitted 27 October, 2025; originally announced October 2025.

Comments: 31 pages, 2 figures

Quantum Transparency of Near-extremal Black Holes

Authors: Roberto Emparan, Stefano Trezzi

Abstract: We investigate the scattering of electromagnetic and gravitational waves off a Reissner-Nordström black hole in the low-temperature regime where the near-horizon throat experiences large quantum fluctuations. We find that the black hole is transparent to electromagnetic and gravitational radiation of fixed helicity below a certain frequency threshold. This phenomenon arises because the angular mom… ▽ More We investigate the scattering of electromagnetic and gravitational waves off a Reissner-Nordström black hole in the low-temperature regime where the near-horizon throat experiences large quantum fluctuations. We find that the black hole is transparent to electromagnetic and gravitational radiation of fixed helicity below a certain frequency threshold. This phenomenon arises because the angular momentum of the black hole is quantized, creating an energy gap between the spinless black hole state and the first excited spinning states. Radiation with angular momentum -- such as photons, gravitons, and partial waves of a massless scalar field, which we also study -- must supply enough energy to bridge this gap to be absorbed. Below this threshold, no absorption can occur, rendering the black hole transparent. For frequencies above the gap, the scarcity of black hole states continues to suppress the absorption cross-section relative to semiclassical predictions, making the black hole translucent rather than completely transparent. Notably, electromagnetic absorption is significantly stronger than gravitational absorption, beyond what differences in spin alone would suggest. △ Less

Submitted 4 October, 2025; v1 submitted 4 July, 2025; originally announced July 2025.

Comments: 22 pages, 8 figures. v2: 23 pages, 8 figures. Small improvements, incl mention of di-quanta absorption, and refined quantum vs semiclassical comparison. v3: added comment. Matches published version

Journal ref: JHEP 10 (2025) 23

Quantum Cross-section of Near-extremal Black Holes

Authors: Roberto Emparan

Abstract: We explore how to detect the large quantum fluctuations in the throat of a near-extremal black hole, where the dynamics are governed by the Schwarzian theory. To this end, we scatter a low-frequency wave of a massless, minimal scalar off the black hole and calculate the absorption cross-section. In the semiclassical regime, where the Schwarzian is weakly coupled, we recover the universal result th… ▽ More We explore how to detect the large quantum fluctuations in the throat of a near-extremal black hole, where the dynamics are governed by the Schwarzian theory. To this end, we scatter a low-frequency wave of a massless, minimal scalar off the black hole and calculate the absorption cross-section. In the semiclassical regime, where the Schwarzian is weakly coupled, we recover the universal result that the cross-section equals the horizon area. However, in the strongly coupled regime, where quantum fluctuations dominate, we find that the absorption cross-section exceeds the semiclassical prediction. This result may seem counterintuitive, given that the density of black hole states is suppressed in this regime. Nevertheless, two effects outweigh this suppression. First, quantum fluctuations enhance absorption transitions between individual states, with the effect becoming stronger closer to the ground state. Second, these fluctuations significantly reduce stimulated emission. We conclude that a measurement showing an enhanced absorption cross-section serves as a clear signature of the large quantum fluctuations in the geometry. △ Less

Submitted 18 April, 2025; v1 submitted 29 January, 2025; originally announced January 2025.

Comments: 16 pages, 3 figures. v2: minor changes. v3: small improvements and refs added. Matches published version

Journal ref: JHEP 04 (2025) 122

String Theory in a Pinch: Resolving the Gregory-Laflamme Singularity

Authors: Roberto Emparan, Mikel Sanchez-Garitaonandia, Marija Tomašević

Abstract: Thin enough black strings are unstable to growing ripples along their length, eventually pinching and forming a naked singularity on the horizon. We investigate how string theory can resolve this singularity. First, we study the string-scale version of the static non-uniform black strings that branch off at the instability threshold: "string-ball strings", which are linearly extended, self-gravita… ▽ More Thin enough black strings are unstable to growing ripples along their length, eventually pinching and forming a naked singularity on the horizon. We investigate how string theory can resolve this singularity. First, we study the string-scale version of the static non-uniform black strings that branch off at the instability threshold: "string-ball strings", which are linearly extended, self-gravitating configurations of string balls obtained in the Horowitz-Polchinski (HP) approach to near-Hagedorn string states. We construct non-uniform HP strings in spatial dimensions $d\leq 6$ and show that, as the inhomogeneity increases, they approach localized HP balls. We also examine the thermodynamic properties of the different phases in the canonical and microcanonical ensembles. We find that, for a sufficiently small mass, the uniform HP string will be stable and not evolve into a non-uniform or localized configuration. Building on these results and independent evidence from the evolution of the black string instability with $α'$ corrections, we propose that, at least in $d=4,5$, string theory slows and eventually halts the pinching evolution at a classically stable stringy neck. In $d\geq 6$ this transition is likely to occur into a puffed-up string ball. The system then enters a slower phase in which the neck gradually evaporates into radiation. We discuss this scenario as a framework for understanding how string theory resolves the formation of naked singularities. △ Less

Submitted 27 February, 2025; v1 submitted 22 November, 2024; originally announced November 2024.

Comments: 34 pages, 9 figures. v2: revised and improved discussion of stability. 38 pages, 10 figures. v3: matches published version

Report number: CPHT-RR082.112024

Journal ref: JHEP 02 (2025) 104

Black Holes Inside and Out 2024: visions for the future of black hole physics

Authors: Niayesh Afshordi, Abhay Ashtekar, Enrico Barausse, Emanuele Berti, Richard Brito, Luca Buoninfante, Raúl Carballo-Rubio, Vitor Cardoso, Gregorio Carullo, Mihalis Dafermos, Mariafelicia De Laurentis, Adrian del Rio, Francesco Di Filippo, Astrid Eichhorn, Roberto Emparan, Ruth Gregory, Carlos A. R. Herdeiro, Jutta Kunz, Luis Lehner, Stefano Liberati, Samir D. Mathur, Samaya Nissanke, Paolo Pani, Alessia Platania, Frans Pretorius , et al. (5 additional authors not shown)

Abstract: The gravitational physics landscape is evolving rapidly, driven by our ability to study strong-field regions, in particular black holes. Black Holes Inside and Out gathered world experts to discuss the status of the field and prospects ahead. We hope that the ideas and perspectives are a source of inspiration. Structure: Black Hole Evaporation - 50 Years by William Unruh The Stability Problem… ▽ More The gravitational physics landscape is evolving rapidly, driven by our ability to study strong-field regions, in particular black holes. Black Holes Inside and Out gathered world experts to discuss the status of the field and prospects ahead. We hope that the ideas and perspectives are a source of inspiration. Structure: Black Hole Evaporation - 50 Years by William Unruh The Stability Problem for Extremal Black Holes by Mihalis Dafermos The Entropy of Black Holes by Robert M. Wald The Non-linear Regime of Gravity by Luis Lehner Black Holes Galore in D > 4 by Roberto Emparan Same as Ever: Looking for (In)variants in the Black Holes Landscape by Carlos A. R. Herdeiro Black Holes, Cauchy Horizons, and Mass Inflation by Matt Visser The Backreaction Problem for Black Holes in Semiclassical Gravity by Adrian del Rio Black Holes Beyond General Relativity by Enrico Barausse and Jutta Kunz Black Holes as Laboratories: Searching for Ultralight Fields by Richard Brito Primordial Black Holes from Inflation by Misao Sasaki Tests of General Relativity with Future Detectors by Emanuele Berti Black Holes as Laboratories: Tests of General Relativity by Ruth Gregory and Samaya Nissanke Simulating Black Hole Imposters by Frans Pretorius Black Hole Spectroscopy: Status Report by Gregorio Carullo VLBI as a Precision Strong Gravity Instrument by Paul Tiede Testing the nature of compact objects and the black hole paradigm by Mariafelicia De Laurentis and Paolo Pani Some Thoughts about Black Holes in Asymptotic Safety by Alessia Platania Black Hole Evaporation in Loop Quantum Gravity by Abhay Ashtekar How the Black Hole Puzzles are Resolved in String Theory by Samir D. Mathur Quantum Black Holes: From Regularization to Information Paradoxes by Niayesh Afshordi and Stefano Liberati △ Less

Submitted 18 October, 2024; originally announced October 2024.

Comments: 221 pages, 21 contributions

Chemical Potential and Charge in Quantum Black Holes

Authors: Ana Climent, Roberto Emparan, Robie A. Hennigar

Abstract: We study systems in $2+1$ dimensions consisting of defects that source an electric charge, or a magnetic flux, of a $U(1)$ field, and we use holography to compute their effects on quantum conformal fields. We can also hide the defects inside the horizon of a black hole, where they continue to affect the quantum fields outside. By extending the solutions to braneworld holography, we find the non-li… ▽ More We study systems in $2+1$ dimensions consisting of defects that source an electric charge, or a magnetic flux, of a $U(1)$ field, and we use holography to compute their effects on quantum conformal fields. We can also hide the defects inside the horizon of a black hole, where they continue to affect the quantum fields outside. By extending the solutions to braneworld holography, we find the non-linear backreaction of the quantum fields on the defect and black hole backgrounds. This gives quantum charged point particles and black holes. The charged quantum black holes markedly differ from classically charged BTZ black holes, since the quantum-induced electromagnetic field in $2+1$ dimensions has a better asymptotic behavior than its classical counterpart. The construction also gives a new class of (near-)extremal charged quantum black holes with AdS$_2$ throats. △ Less

Submitted 23 April, 2024; originally announced April 2024.

Comments: 30 pages + appendices, 11 figures

Universal Construction of Black Hole Microstates

Authors: Ana Climent, Roberto Emparan, Javier M. Magan, Martin Sasieta, Alejandro Vilar López

Abstract: We refine and extend a recent construction of sets of black hole microstates with semiclassical interiors that span a Hilbert space of dimension $e^S$, where $S$ is the black hole entropy. We elaborate on the definition and properties of microstates in statistical and black hole mechanics. The gravitational description of microstates employs matter shells in the interior of the black hole, and we… ▽ More We refine and extend a recent construction of sets of black hole microstates with semiclassical interiors that span a Hilbert space of dimension $e^S$, where $S$ is the black hole entropy. We elaborate on the definition and properties of microstates in statistical and black hole mechanics. The gravitational description of microstates employs matter shells in the interior of the black hole, and we argue that in the limit where the shells are very heavy, the construction acquires universal validity. To this end, we show it for very wide classes of black holes: we first extend the construction to rotating and charged black holes, including extremal and near-extremal solutions, with or without supersymmetry, and we sketch how the construction of microstates can be embedded in String Theory. We then describe how the approach can include general quantum corrections, near or far from extremality. For supersymmetric black holes, the microstates we construct differ from other recent constructions in that the interior excitations are not confined within the near-extremal throat. △ Less

Submitted 2 February, 2024; v1 submitted 16 January, 2024; originally announced January 2024.

Comments: 17 pages + appendices; v2: typos corrected, references added, added paragraph at the end of Sec. VB

The correspondence between rotating black holes and fundamental strings

Authors: Nejc Čeplak, Roberto Emparan, Andrea Puhm, Marija Tomašević

Abstract: The correspondence principle between strings and black holes is a general framework for matching black holes and massive states of fundamental strings at a point where their physical properties (such as mass, entropy and temperature) smoothly agree with each other. This correspondence becomes puzzling when attempting to include rotation: At large enough spins, there exist degenerate string states… ▽ More The correspondence principle between strings and black holes is a general framework for matching black holes and massive states of fundamental strings at a point where their physical properties (such as mass, entropy and temperature) smoothly agree with each other. This correspondence becomes puzzling when attempting to include rotation: At large enough spins, there exist degenerate string states that seemingly cannot be matched to any black hole. Conversely, there exist black holes with arbitrarily large spins that cannot correspond to any single-string state. We discuss in detail the properties of both types of objects and find that a correspondence that resolves the puzzles is possible by adding dynamical features and non-stationary configurations to the picture. Our scheme incorporates all black hole and string phases as part of the correspondence, save for one outlier which remains enigmatic: the near-extremal Kerr black hole. Along the way, we elaborate on general aspects of the correspondence that have not been emphasized before. △ Less

Submitted 3 December, 2023; v1 submitted 7 July, 2023; originally announced July 2023.

Comments: 48 pages, 11 figures. v2: 50 pages, 11 figures. Added discussion of ensembles in the correspondence and other smaller improvements. v3: published version

Report number: CPHT-RR037.072023

Journal ref: JHEP 11 (2023) 226

Black holes in the classical and quantum world

Authors: Roberto Emparan, Elvis Barakovic, Roukaya Dekhil, Filip Rescic

Abstract: These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black hole (classical and quantum fields, with little astrophysics). We aim more at qualitative, intuitive understanding than at quantitative rigor or detail. Accordi… ▽ More These are the lecture notes for an introductory course on black holes and some aspects of their interaction with the classical and quantum world. The focus is on phenomena of "fundamental physics" in the immediate surroundings of the black hole (classical and quantum fields, with little astrophysics). We aim more at qualitative, intuitive understanding than at quantitative rigor or detail. Accordingly, we only assume previous exposure to a conventional introduction to the elements of General Relativity and a glancing acquaintance with the Schwarzschild solution, but not more. We use many figures for illustrations and provide a set of carefully guided exercises. Topics: (1) The black hole as a tale of light and darkness. (2) The black hole that vibrates. (3) The black hole that rotates. (4) The black hole that evaporates. (A) Guided problems. △ Less

Submitted 2 October, 2023; v1 submitted 19 June, 2023; originally announced June 2023.

Comments: Lectures at Second Training School of COST Action "Quantum gravity phenomenology in the multi-messenger approach", to be published in PoS. 51 pages, 17 figures. v2: minor corrections, final version

Journal ref: PoS (QG-MMSchools) 004 (2023)

Holographic duals of evaporating black holes

Authors: Roberto Emparan, Raimon Luna, Ryotaku Suzuki, Marija Tomašević, Benson Way

Abstract: We describe the dynamical evaporation of a black hole as the classical evolution in time of a black hole in an Anti-de Sitter braneworld. A bulk black hole whose horizon intersects the brane yields the classical bulk dual of a black hole coupled to quantum conformal fields. The evaporation of this black hole happens when the bulk horizon slides off the brane, making the horizon on the brane shrink… ▽ More We describe the dynamical evaporation of a black hole as the classical evolution in time of a black hole in an Anti-de Sitter braneworld. A bulk black hole whose horizon intersects the brane yields the classical bulk dual of a black hole coupled to quantum conformal fields. The evaporation of this black hole happens when the bulk horizon slides off the brane, making the horizon on the brane shrink. We use a large-D effective theory of the bulk Einstein equations to solve the time evolution of these systems. With this method, we study the dual evaporation of a variety of black holes interacting with colder radiation baths. We also obtain the dual of the collapse of holographic radiation to form a black hole on the brane. Finally, we discuss the evolution of the Page curve of the radiation in our evaporation setups, with entanglement islands appearing and then shrinking during the decreasing part of the curve. △ Less

Submitted 28 May, 2023; v1 submitted 6 January, 2023; originally announced January 2023.

Comments: 27 pages, 13 figures. v2: 31 pages, 16 figures. Improved discussions, refs added. v3: matches published version

Report number: CPHT-RR057.112022, TTI-MATHPHYS-18

Journal ref: JHEP05(2023)182

Black holes in dS$_3$

Authors: Roberto Emparan, Juan F. Pedraza, Andrew Svesko, Marija Tomašević, Manus R. Visser

Abstract: In three-dimensional de Sitter space classical black holes do not exist, and the Schwarzschild-de Sitter solution instead describes a conical defect with a single cosmological horizon. We argue that the quantum backreaction of conformal fields can generate a black hole horizon, leading to a three-dimensional quantum de Sitter black hole. Its size can be as large as the cosmological horizon in a Na… ▽ More In three-dimensional de Sitter space classical black holes do not exist, and the Schwarzschild-de Sitter solution instead describes a conical defect with a single cosmological horizon. We argue that the quantum backreaction of conformal fields can generate a black hole horizon, leading to a three-dimensional quantum de Sitter black hole. Its size can be as large as the cosmological horizon in a Nariai-type limit. We show explicitly how these solutions arise using braneworld holography, but also compare to a non-holographic, perturbative analysis of backreaction due to conformally coupled scalar fields in conical de Sitter space. We analyze the thermodynamics of this quantum black hole, revealing it behaves similarly to its classical four-dimensional counterpart, where the generalized entropy replaces the classical Bekenstein-Hawking entropy. We compute entropy deficits due to nucleating the three-dimensional black hole and revisit arguments for a possible matrix model description of dS spacetimes. Finally, we comment on the holographic dual description for dS spacetimes as seen from the braneworld perspective. △ Less

Submitted 21 November, 2022; v1 submitted 7 July, 2022; originally announced July 2022.

Comments: 43 pages plus appendices, 12 figures. v2: footnote expanded into an appendix, comments and references added. v3: minor edits, references added, JHEP version

Report number: IFT-UAM/CSIC-22-63, CPHT-RR045.062022

Higher-curvature Gravities from Braneworlds and the Holographic c-theorem

Authors: Pablo Bueno, Roberto Emparan, Quim Llorens

Abstract: We study the structure of the higher-curvature gravitational densities that are induced from holographic renormalization in AdS$_{d+1}$. In a braneworld construction, such densities define a d-dimensional higher-curvature gravitational theory on the brane, which in turn is dual to a (d-1)-dimensional CFT living at its boundary. We show that this CFT$_{d-1}$ satisfies a holographic c-theorem in gen… ▽ More We study the structure of the higher-curvature gravitational densities that are induced from holographic renormalization in AdS$_{d+1}$. In a braneworld construction, such densities define a d-dimensional higher-curvature gravitational theory on the brane, which in turn is dual to a (d-1)-dimensional CFT living at its boundary. We show that this CFT$_{d-1}$ satisfies a holographic c-theorem in general dimensions (different than the g-theorem of holographic boundary CFTs), since at each and every order the higher-curvature densities satisfy c-theorems on their own. We find that, in these densities, the terms that affect the monotonicity of the holographic c-function are algebraic in the curvature, and do not involve covariant derivatives of the Riemann tensor. We examine various other features of the holographically induced higher-curvature densities, such as the presence of reduced-order traced equations, and their connection to Born-Infeld-type gravitational Lagrangians. △ Less

Submitted 1 February, 2023; v1 submitted 28 April, 2022; originally announced April 2022.

Comments: 30 pages, 1 figure. Mathematica notebook included in source contains quintic and sextic counterterms

Report number: CERN-TH-2022-076

Journal ref: Phys. Rev. D 106, 044012 (2022)

Bubbles of nothing in binary black holes and black rings, and viceversa

Authors: Marco Astorino, Roberto Emparan, Adriano Viganò

Abstract: We argue that expanding bubbles of nothing are a widespread feature of systems of black holes with multiple or non-spherical horizons, appearing as a limit of regions that are narrowly enclosed by the horizons. The bubble is a minimal cycle that links the Einstein-Rosen bridges in the system, and its expansion occurs through the familiar stretching of space in black hole interiors. We demonstrate… ▽ More We argue that expanding bubbles of nothing are a widespread feature of systems of black holes with multiple or non-spherical horizons, appearing as a limit of regions that are narrowly enclosed by the horizons. The bubble is a minimal cycle that links the Einstein-Rosen bridges in the system, and its expansion occurs through the familiar stretching of space in black hole interiors. We demonstrate this idea (which does not involve any Wick rotations) with explicit constructions in four and five dimensions. The geometries of expanding bubbles in these dimensions arise as a limit of, respectively, static black hole binaries and black rings. The limit is such that the separation between the two black holes, or the inner hole of the black ring, becomes very small, and the horizons of the black holes correspond to acceleration horizons of the bubbles. We also explain how a five-dimensional black hole binary gives rise to a different type of expanding bubble. We then show that bubble spacetimes can host black hole binaries and black rings in static equilibrium, with their gravitational attraction being balanced against the background spacetime expansion. Similar constructions are expected in six or more dimensions, but most of these solutions can be obtained only numerically. Finally, we argue that the Nariai solution can be regarded as containing an expanding circular bubble of nothing. △ Less

Submitted 2 July, 2022; v1 submitted 20 April, 2022; originally announced April 2022.

Comments: 23 pages, 11 figures. v2: minor changes (incl in the title); added discussion on Nariai solution as a bubble of nothing. v3: matches published version

Report number: IFUM-1094-FT

Journal ref: JHEP07(2022)007

Black Tsunamis and Naked Singularities in AdS

Authors: Roberto Emparan, David Licht, Ryotaku Suzuki, Marija Tomašević, Benson Way

Abstract: We study the evolution of the Gregory-Laflamme instability for black strings in global AdS spacetime, and investigate the CFT dual of the formation of a bulk naked singularity. Using an effective theory in the large D limit, we uncover a rich variety of dynamical behaviour, depending on the thickness of the string and on initial perturbations. These include: large inflows of horizon generators fro… ▽ More We study the evolution of the Gregory-Laflamme instability for black strings in global AdS spacetime, and investigate the CFT dual of the formation of a bulk naked singularity. Using an effective theory in the large D limit, we uncover a rich variety of dynamical behaviour, depending on the thickness of the string and on initial perturbations. These include: large inflows of horizon generators from the asymptotic boundary (a `black tsunami'); a pinch-off of the horizon that likely reveals a naked singularity; and competition between these two behaviours, such as a nakedly singular pinch-off that subsequently gets covered by a black tsunami. The holographic dual describes different patterns of heat flow due to the Hawking radiation of two black holes placed at the antipodes of a spherical universe. We also present a model that describes, in any D, the burst in the holographic stress-energy tensor when the signal from a bulk self-similar naked singularity reaches the boundary. The model shows that the shear components of the boundary stress diverge in finite time, while the energy density and pressures from the burst vanish. △ Less

Submitted 15 February, 2022; v1 submitted 15 December, 2021; originally announced December 2021.

Comments: 30 pages, 7 figures. v2: minor typos fixed. Matches published version

Report number: CPHT-RR107.122021, TTI-MATHPHYS-8

Journal ref: J. High Energ. Phys. 2022, 90 (2022)

Holographic Complexity of Quantum Black Holes

Authors: Roberto Emparan, Antonia Micol Frassino, Martin Sasieta, Marija Tomašević

Abstract: We analyze different holographic complexity proposals for black holes that include corrections from bulk quantum fields. The specific setup is the quantum BTZ black hole, which encompasses in an exact manner the effects of conformal fields with large central charge in the presence of the black hole, including the backreaction corrections to the BTZ metric. Our results show that Volume Complexity a… ▽ More We analyze different holographic complexity proposals for black holes that include corrections from bulk quantum fields. The specific setup is the quantum BTZ black hole, which encompasses in an exact manner the effects of conformal fields with large central charge in the presence of the black hole, including the backreaction corrections to the BTZ metric. Our results show that Volume Complexity admits a consistent quantum expansion and correctly reproduces known limits. On the other hand, the generalized Action Complexity picks up large contributions from the singularity, which is modified due to quantum backreaction, with the result that Action Complexity does not reproduce the expected classical limit. Furthermore, we show that the doubly-holographic setup allows computing the complexity coming purely from quantum fields - a notion that has proven evasive in usual holographic setups. We find that in holographic induced-gravity scenarios the complexity of quantum fields in a black hole background vanishes to leading order in the gravitational strength of CFT effects. △ Less

Submitted 3 March, 2022; v1 submitted 9 December, 2021; originally announced December 2021.

Comments: 45 pages, 8 figures

Journal ref: JHEP 02 (2022) 204

Quantum Backreaction on Chronology Horizons

Authors: Roberto Emparan, Marija Tomašević

Abstract: We extend in two directions our recent investigation of strongly interacting quantum fields in a class of spacetimes with chronology horizons (Misner spacetimes). First, we generalize to arbitrary dimensions the holographic mechanism of chronology protection in the absence of gravitational backreaction. The AdS geometry dual to a conformal field theory in these spacetimes shows, in every dimension… ▽ More We extend in two directions our recent investigation of strongly interacting quantum fields in a class of spacetimes with chronology horizons (Misner spacetimes). First, we generalize to arbitrary dimensions the holographic mechanism of chronology protection in the absence of gravitational backreaction. The AdS geometry dual to a conformal field theory in these spacetimes shows, in every dimension, an entire separation between the bulk duals of the chronal and non-chronal regions, with the former being complete, regular geometries. In some instances the protection requires the inclusion of non-planar CFT corrections, which we obtain using double holography. Second, we compute the gravitational backreaction of the quantum fields in the Misner-AdS$_3$ spacetime, and show that the null chronology horizon turns into a strong, spacelike curvature singularity. This is one of the few controlled, explicit examples where we can see quantum effects change a Cauchy horizon into a spacelike singularity. △ Less

Submitted 24 September, 2021; v1 submitted 8 September, 2021; originally announced September 2021.

Comments: 18 pages. v2: 21 pages, 1 figure. Added section on double holography and non-planar CFT effects

Journal ref: JHEP 02 (2022) 182

Holography of time machines

Authors: Roberto Emparan, Marija Tomašević

Abstract: We use holography to examine the response of interacting quantum fields to the appearance of closed timelike curves in a dynamically evolving background that initially does not contain them. For this purpose, we study a family of two-dimensional spacetimes that model very broad classes of wormhole time machines. The behavior of strongly coupled conformal theories in these spacetimes is then hologr… ▽ More We use holography to examine the response of interacting quantum fields to the appearance of closed timelike curves in a dynamically evolving background that initially does not contain them. For this purpose, we study a family of two-dimensional spacetimes that model very broad classes of wormhole time machines. The behavior of strongly coupled conformal theories in these spacetimes is then holographically described by three-dimensional AdS bulk geometries that we explicitly construct. The dual bulk spacetime is free from any divergences, but splits into two disconnected components, without and with CTCs, which are joined only through the boundary; then, passages across the chronology horizon are impossible for any field excitations. In dual terms, the strong self-interaction of the CFT decouples the pathological part from the rest of the spacetime. We also find that entangling the CFTs in two separate time machines connects them through a traversable bulk wormhole. Nevertheless, any entanglement-assisted chronology violations will be prevented by quantum bulk corrections, i.e., subleading 1/N effects, again without needing any gravitational backreaction of the CFT. We are led to speculate that chronology may be protected without involving Planck scale physics. △ Less

Submitted 3 April, 2022; v1 submitted 29 July, 2021; originally announced July 2021.

Comments: 31 pages, 3 figures. v2: 32 pages, 5 figures; substantially improved discussion and analysis. v3: 33 pages, 5 figures; revised intro. Matches published version

Journal ref: JHEP 03 (2022) 212

Multi-mouth Traversable Wormholes

Authors: Roberto Emparan, Brianna Grado-White, Donald Marolf, Marija Tomasevic

Abstract: We describe the construction of traversable wormholes with multiple mouths in four spacetime dimensions and discuss associated quantum entanglement. Our wormholes may be traversed between any pair of mouths. In particular, in the three-mouth case they have fundamental group $F_2$ (the free group on two generators). By contrast, connecting three regions $A,B,C$ in pairs ($AB$, $BC$, and $AC$) using… ▽ More We describe the construction of traversable wormholes with multiple mouths in four spacetime dimensions and discuss associated quantum entanglement. Our wormholes may be traversed between any pair of mouths. In particular, in the three-mouth case they have fundamental group $F_2$ (the free group on two generators). By contrast, connecting three regions $A,B,C$ in pairs ($AB$, $BC$, and $AC$) using three separate wormholes would give fundamental group $F_3$. Our solutions are asymptotically flat up to the presence of possible magnetic fluxes or cosmic strings that extend to infinity. The construction begins with a two-mouth traversable wormhole supported by backreaction from quantum fields. Inserting a sufficiently small black hole into its throat preserves traversability between the original two mouths. This black hole is taken to be the mouth of another wormhole connecting the original throat to a new distant region of spacetime. Making the new wormhole traversable in a manner similar to the original two-mouth wormhole provides the desired causal connections. From a dual field theory point of view, when AdS asymptotics are added to our construction, multiparty entanglement may play an important role in the traversability of the resulting wormhole. △ Less

Submitted 2 April, 2021; v1 submitted 14 December, 2020; originally announced December 2020.

Comments: 24 pages, 8 figures. v2: 28 pages; added a section and an appendix on lowering a small black hole down the wormhole throat

Journal ref: JHEP 05 (2021) 032

Quantum BTZ black hole

Authors: Roberto Emparan, Antonia Micol Frassino, Benson Way

Abstract: We study a holographic construction of quantum rotating BTZ black holes that incorporates the exact backreaction from strongly coupled quantum conformal fields. It is based on an exact four-dimensional solution for a black hole localized on a brane in AdS$_4$, first discussed some years ago but never fully investigated in this manner. Besides quantum CFT effects and their backreaction, we also inv… ▽ More We study a holographic construction of quantum rotating BTZ black holes that incorporates the exact backreaction from strongly coupled quantum conformal fields. It is based on an exact four-dimensional solution for a black hole localized on a brane in AdS$_4$, first discussed some years ago but never fully investigated in this manner. Besides quantum CFT effects and their backreaction, we also investigate the role of higher-curvature corrections in the effective three-dimensional theory. We obtain the quantum-corrected geometry and the renormalized stress tensor. We show that the quantum black hole entropy, which includes the entanglement of the fields outside the horizon, satisfies the first law of thermodynamics exactly, even in the presence of backreaction and with higher-curvature corrections, while the Bekenstein-Hawking-Wald entropy does not. This result, which involves a rather non-trivial bulk calculation, shows the consistency of the holographic interpretation of braneworlds. We compare our renormalized stress tensor to results derived for free conformal fields, and for a previous holographic construction without backreaction effects, which is shown to be a limit of the solutions in this article. △ Less

Submitted 26 November, 2020; v1 submitted 31 July, 2020; originally announced July 2020.

Comments: 39 pages, 8 figures. v2: 44 pages. Important revision and improvements, including higher-curvature corrections in the effective theory and Wald entropy. v3: 45 pages. Additional improvements, matches published version

Journal ref: JHEP 11 (2020) 137

Entropy production and entropic attractors in black hole fusion and fission

Authors: Tomas Andrade, Roberto Emparan, Aron Jansen, David Licht, Raimon Luna, Ryotaku Suzuki

Abstract: We study how black hole entropy is generated and the role it plays in several highly dynamical processes: the decay of unstable black strings and ultraspinning black holes; the fusion of two rotating black holes; and the subsequent fission of the merged system into two black holes that fly apart (which can occur in dimension $D\geq 6$, with a mild violation of cosmic censorship). Our approach uses… ▽ More We study how black hole entropy is generated and the role it plays in several highly dynamical processes: the decay of unstable black strings and ultraspinning black holes; the fusion of two rotating black holes; and the subsequent fission of the merged system into two black holes that fly apart (which can occur in dimension $D\geq 6$, with a mild violation of cosmic censorship). Our approach uses the effective theory of black holes at $D\to\infty$, but we expect our main conclusions to hold at finite $D$. Black hole fusion is highly irreversible, while fission, which follows the pattern of the decay of black strings, generates comparatively less entropy. In $2\to 1\to 2$ black hole collisions an intermediate, quasi-thermalized state forms that then fissions. This intermediate state erases much of the memory of the initial states and acts as an attractor funneling the evolution of the collision towards a small subset of outgoing parameters, which is narrower the closer the total angular momentum is to the critical value for fission. Entropy maximization provides a very good guide for predicting the final outgoing states. Along our study, we clarify how entropy production and irreversibility appear in the large $D$ effective theory. We also extend the study of the stability of new black hole phases (black bars and dumbbells). Finally, we discuss entropy production through charge diffusion in collisions of charged black holes. △ Less

Submitted 11 June, 2020; v1 submitted 29 May, 2020; originally announced May 2020.

Comments: 40 pages, 13 figures. v2: small improvements and minor corrections to the text, figures, and references

Journal ref: J. High Energ. Phys. (2020) 2020: 98

Predictivity lost, predictivity regained: a Miltonian cosmic censorship conjecture

Authors: Roberto Emparan

Abstract: Cosmic censorship is known to fail in some well-controlled phenomena, calling into question the predictive power of General Relativity and opening up the possibility of observing Planck-scale physics. We propose that the cosmic censorship conjecture can be amended so that its spirit prevails. Naked singularities that, classically, have zero mass are allowed. Physically, these are Planck-sized `bla… ▽ More Cosmic censorship is known to fail in some well-controlled phenomena, calling into question the predictive power of General Relativity and opening up the possibility of observing Planck-scale physics. We propose that the cosmic censorship conjecture can be amended so that its spirit prevails. Naked singularities that, classically, have zero mass are allowed. Physically, these are Planck-sized `black holes', which evaporate in a few Planck times. General Relativity fails only for a tiny interval in time, to then quickly regain control in a Miltonian evolution that returns us to the predictive paradise of Einstein's equations. If this refinement of the conjecture is correct, then, even though Nature does allow to expose breakdowns in the smooth fabric of spacetime, it limits them to a mostly harmless minimum. △ Less

Submitted 15 May, 2020; originally announced May 2020.

Comments: 6 pages. Essay for the Gravity Research Foundation 2020 Awards

Journal ref: Int.J.Mod.Phys.D 29 (2020) 14, 2043021

Precursory collapse in Neutron Star-Black Hole mergers

Authors: Roberto Emparan, Daniel Marin

Abstract: We investigate the properties of the event horizon in the merger between a large black hole and a smaller neutron star. We find that, if the star is compact enough, then, in its rest frame a horizon begins to grow inside the star before it merges with the black hole, in a manner analogous to the growth of the event horizon in stellar collapse. We may say that, ahead of its fall into the larger bla… ▽ More We investigate the properties of the event horizon in the merger between a large black hole and a smaller neutron star. We find that, if the star is compact enough, then, in its rest frame a horizon begins to grow inside the star before it merges with the black hole, in a manner analogous to the growth of the event horizon in stellar collapse. We may say that, ahead of its fall into the larger black hole, the neutron star begins to become a black hole itself. We discuss how the phenomenon, even if not directly observable, can be invariantly characterized. We demonstrate it quantitatively by explicitly constructing the merger event horizon in the extreme-mass-ratio limit. We show that the effect is present for realistic neutron star models and admissible values of the compactness. △ Less

Submitted 1 July, 2020; v1 submitted 17 April, 2020; originally announced April 2020.

Comments: 13 pages, 16 figures. v2: minor clarifications and added references. Matches published version

Journal ref: Phys. Rev. D 102, 024009 (2020)

The Large D Limit of Einstein's Equations

Authors: Roberto Emparan, Christopher P. Herzog

Abstract: We review recent progress in taking the large dimension limit of Einstein's equations. Most of our analysis is classical in nature and concerns situations where there is a black hole horizon although we briefly discuss various extensions that include quantum gravitational effects. The review consists of two main parts: the first a discussion of general aspects of black holes and effective membrane… ▽ More We review recent progress in taking the large dimension limit of Einstein's equations. Most of our analysis is classical in nature and concerns situations where there is a black hole horizon although we briefly discuss various extensions that include quantum gravitational effects. The review consists of two main parts: the first a discussion of general aspects of black holes and effective membrane theories in this large dimension limit, and the second a series of applications of this limit to interesting physical problems. The first part includes a discussion of quasinormal modes which leads naturally into a description of effective hydrodynamic-like equations that describe the near horizon geometry. There are two main approaches to these effective theories -- a fully covariant approach and a partially gauge-fixed one -- which we discuss in relation to each other. In the second part we divide the applications up into three main categories: the Gregory-Laflamme instability, black hole collisions and mergers, and the anti-de Sitter/conformal field theory correspondence (AdS/CFT). AdS/CFT posits an equivalence between a gravitational theory and a strongly interacting field theory, allowing us to extend our spectrum of applications to problems in hydrodynamics, condensed matter physics, and nuclear physics. A final, shorter part of the review describes further promising directions where there have been, as yet, few published research articles. △ Less

Submitted 25 March, 2020; originally announced March 2020.

Comments: 59 pages, 10 figures; formatted for submission as a review to RMP; please send us feedback

Journal ref: Rev. Mod. Phys. 92, 45005 (2020)

Strong cosmic censorship in the BTZ black hole

Authors: Roberto Emparan, Marija Tomašević

Abstract: Recently it has been shown that quantum fields can be regular on the inner, Cauchy horizon of a rotating BTZ black hole, which appears to indicate a failure of strong cosmic censorship. We argue that, instead, what these results imply is that the inner horizon remains non-singular when leading-order backreaction of the quantum fields is computed, but, after next-order backreaction is accounted for… ▽ More Recently it has been shown that quantum fields can be regular on the inner, Cauchy horizon of a rotating BTZ black hole, which appears to indicate a failure of strong cosmic censorship. We argue that, instead, what these results imply is that the inner horizon remains non-singular when leading-order backreaction of the quantum fields is computed, but, after next-order backreaction is accounted for, it will become singular. Then, strong cosmic censorship will be enforced in the BTZ black hole. We support our claims using a four-dimensional holographic dual of the system, which connects the instability of the inner horizon of the BTZ black hole to that of Kerr-type black holes. △ Less

Submitted 8 June, 2020; v1 submitted 5 February, 2020; originally announced February 2020.

Comments: 9 pages. v2: minor changes. Matches published version

Journal ref: JHEP 06 (2020) 038

Prospects for Fundamental Physics with LISA

Authors: Enrico Barausse, Emanuele Berti, Thomas Hertog, Scott A. Hughes, Philippe Jetzer, Paolo Pani, Thomas P. Sotiriou, Nicola Tamanini, Helvi Witek, Kent Yagi, Nicolas Yunes, T. Abdelsalhin, A. Achucarro, K. V. Aelst, N. Afshordi, S. Akcay, L. Annulli, K. G. Arun, I. Ayuso, V. Baibhav, T. Baker, H. Bantilan, T. Barreiro, C. Barrera-Hinojosa, N. Bartolo , et al. (296 additional authors not shown)

Abstract: In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA, we present here a sample of what we view as particularly promising directions, based in part on the current research interests of the LISA sc… ▽ More In this paper, which is of programmatic rather than quantitative nature, we aim to further delineate and sharpen the future potential of the LISA mission in the area of fundamental physics. Given the very broad range of topics that might be relevant to LISA, we present here a sample of what we view as particularly promising directions, based in part on the current research interests of the LISA scientific community in the area of fundamental physics. We organize these directions through a "science-first" approach that allows us to classify how LISA data can inform theoretical physics in a variety of areas. For each of these theoretical physics classes, we identify the sources that are currently expected to provide the principal contribution to our knowledge, and the areas that need further development. The classification presented here should not be thought of as cast in stone, but rather as a fluid framework that is amenable to change with the flow of new insights in theoretical physics. △ Less

Submitted 27 April, 2020; v1 submitted 27 January, 2020; originally announced January 2020.

Comments: 22 pages, 1 figure, to appear in General Relativity and Gravitation

Journal ref: Gen.Rel.Grav. 52 (2020) 8, 81

Black hole collisions, instabilities, and cosmic censorship violation at large D

Authors: Tomas Andrade, Roberto Emparan, David Licht, Raimon Luna

Abstract: We study the evolution of black hole collisions and ultraspinning black hole instabilities in higher dimensions. These processes can be efficiently solved numerically in an effective theory in the limit of large number of dimensions D. We present evidence that they lead to violations of cosmic censorship. The post-merger evolution of the collision of two black holes with total angular momentum abo… ▽ More We study the evolution of black hole collisions and ultraspinning black hole instabilities in higher dimensions. These processes can be efficiently solved numerically in an effective theory in the limit of large number of dimensions D. We present evidence that they lead to violations of cosmic censorship. The post-merger evolution of the collision of two black holes with total angular momentum above a certain value is governed by the properties of a resonance-like intermediate state: a long-lived, rotating black bar, which pinches off towards a naked singularity due to an instability akin to that of black strings. We compute the radiative loss of spin for a rotating bar using the quadrupole formula at finite D, and argue that at large enough D ---very likely for $D\gtrsim 8$, but possibly down to D=6--- the spin-down is too inefficient to quench this instability. We also study the instabilities of ultraspinning black holes by solving numerically the time evolution of axisymmetric and non-axisymmetric perturbations. We demonstrate the development of transient black rings in the former case, and of multi-pronged horizons in the latter, which then proceed to pinch and, arguably, fragment into smaller black holes. △ Less

Submitted 16 September, 2019; v1 submitted 9 August, 2019; originally announced August 2019.

Comments: 43 pages, 17 figures

Journal ref: J. High Energ. Phys. (2019) 2019: 99

Topology-changing horizons at large D as Ricci flows

Authors: Roberto Emparan, Ryotaku Suzuki

Abstract: The topology-changing transition between black strings and black holes localized in a Kaluza-Klein circle is investigated in an expansion in the inverse of the number of dimensions D. Performing a new kind of large-D scaling reduces the problem to a Ricci flow of the near-horizon geometry as it varies along the circle direction. The flows of interest here simplify to a non-linear logarithmic diffu… ▽ More The topology-changing transition between black strings and black holes localized in a Kaluza-Klein circle is investigated in an expansion in the inverse of the number of dimensions D. Performing a new kind of large-D scaling reduces the problem to a Ricci flow of the near-horizon geometry as it varies along the circle direction. The flows of interest here simplify to a non-linear logarithmic diffusion equation, with solutions known in the literature which are interpreted as the smoothed conifold geometries involved in the transition, namely, split and fused cones, which connect to black holes and non-uniform black strings away from the conical region. Our study demonstrates the adaptability of the 1/D expansion to deal with all the regimes and aspects of the static black hole/black string system, and provides another instance of the manner in which the large D limit reduces the task of solving Einstein's equations to a simpler but compelling mathematical problem. △ Less

Submitted 22 July, 2019; v1 submitted 3 May, 2019; originally announced May 2019.

Comments: 34 pages, 7 figures; v2: minor corrections, refs added; v3: minor corrections, some comments added

Journal ref: JHEP 07 (2019) 094

Exotic compact objects with soft hair

Authors: Guilherme Raposo, Paolo Pani, Roberto Emparan

Abstract: Motivated by the lack of a general parametrization for exotic compact objects, we construct a class of perturbative solutions valid for small (but otherwise generic) multipolar deviations from a Schwarzschild metric in general relativity. We introduce two classes of exotic compact objects, with "soft" and "hard" hair, for which the curvature at the surface is respectively comparable to or much lar… ▽ More Motivated by the lack of a general parametrization for exotic compact objects, we construct a class of perturbative solutions valid for small (but otherwise generic) multipolar deviations from a Schwarzschild metric in general relativity. We introduce two classes of exotic compact objects, with "soft" and "hard" hair, for which the curvature at the surface is respectively comparable to or much larger than that at the corresponding black-hole horizon. We extend the Hartle-Thorne formalism to relax the assumption of equatorial symmetry and to include deformations induced by multipole moments higher than the spin, thus constructing the most general, axisymmetric quasi-Schwarzschild solution to Einstein's vacuum equations. We explicitly construct several particular solutions of objects with soft hair, which might be useful for tests of quasi-black-hole metrics, and also to study deformed neutron stars. We show that the more compact a soft exotic object is, the less hairy it will be. All its multipole moments can approach their corresponding Kerr values only in two ways as their compactness increases: either logarithmically (or faster) if the moments are spin-induced, or linearly (or faster) otherwise. Our results suggest that it is challenging (but possibly feasible with next-generation gravitational-wave detectors) to distinguish Kerr black holes from a large class of ultracompact exotic objects on the basis of their different multipolar structure. △ Less

Submitted 9 April, 2019; v1 submitted 18 December, 2018; originally announced December 2018.

Comments: 16 pages, 1 figure. Online repository with explicit solutions and embedding diagrams available at https://www.darkgra.org/projects.html ; Version accepted to PRD

Journal ref: Phys. Rev. D 99, 104050 (2019)

Cosmic censorship violation in black hole collisions in higher dimensions

Authors: Tomas Andrade, Roberto Emparan, David Licht, Raimon Luna

Abstract: We argue that cosmic censorship is violated in the collision of two black holes in high spacetime dimension D when the initial total angular momentum is sufficiently large. The two black holes merge and form an unstable bar-like horizon, which grows a neck in its middle that pinches down with diverging curvature. When D is large, the emission of gravitational radiation is strongly suppressed and c… ▽ More We argue that cosmic censorship is violated in the collision of two black holes in high spacetime dimension D when the initial total angular momentum is sufficiently large. The two black holes merge and form an unstable bar-like horizon, which grows a neck in its middle that pinches down with diverging curvature. When D is large, the emission of gravitational radiation is strongly suppressed and cannot spin down the system to a stable rotating black hole before the neck grows. The phenomenon is demonstrated using simple numerical simulations of the effective theory in the 1/D expansion. We propose that, even though cosmic censorship is violated, the loss of predictability is small independently of D. △ Less

Submitted 2 May, 2019; v1 submitted 12 December, 2018; originally announced December 2018.

Comments: 9 pages, 2 figures. v2: matches published version

Journal ref: JHEP 04 (2019) 121

Charged rotating black holes in higher dimensions

Authors: Tomas Andrade, Roberto Emparan, David Licht

Abstract: We use a recent implementation of the large $D$ expansion in order to construct the higher-dimensional Kerr-Newman black hole and also new charged rotating black bar solutions of the Einstein-Maxwell theory, all with rotation along a single plane. We describe the space of solutions, obtain their quasinormal modes, and study the appearance of instabilities as the horizons spread along the plane of… ▽ More We use a recent implementation of the large $D$ expansion in order to construct the higher-dimensional Kerr-Newman black hole and also new charged rotating black bar solutions of the Einstein-Maxwell theory, all with rotation along a single plane. We describe the space of solutions, obtain their quasinormal modes, and study the appearance of instabilities as the horizons spread along the plane of rotation. Generically, the presence of charge makes the solutions less stable. Instabilities can appear even when the angular momentum of the black hole is small, as long as the charge is sufficiently large. We expect that, although our study is performed in the limit $D\to\infty$, the results provide a good approximation for charged rotating black holes at finite $D\geq 6$. △ Less

Submitted 16 October, 2018; originally announced October 2018.

Comments: 21 pages, 1 figure

Journal ref: JHEP 02 (2019) 076

Rotating black holes and black bars at large D

Authors: Tomas Andrade, Roberto Emparan, David Licht

Abstract: We propose and demonstrate a new and efficient approach to investigate black hole dynamics in the limit of large number of dimensions $D$. The basic idea is that an asymptotically flat black brane evolving under the Gregory-Laflamme instability forms lumps that closely resemble a localized black hole. In this manner, the large-$D$ effective equations for extended black branes can be used to study… ▽ More We propose and demonstrate a new and efficient approach to investigate black hole dynamics in the limit of large number of dimensions $D$. The basic idea is that an asymptotically flat black brane evolving under the Gregory-Laflamme instability forms lumps that closely resemble a localized black hole. In this manner, the large-$D$ effective equations for extended black branes can be used to study localized black holes. We show that these equations have exact solutions for black-hole-like lumps on the brane, which correctly capture the main properties of Schwarzschild and Myers-Perry black holes at large $D$, including their slow quasinormal modes and the ultraspinning instabilities (axisymmetric or not) at large angular momenta. Furthermore, we obtain a novel class of rotating `black bar' solutions, which are stationary when $D\to\infty$, and are long-lived when $D$ is finite but large, since their gravitational wave emission is strongly suppressed. The leading large $D$ approximation reproduces to per-cent level accuracy previous numerical calculations of the bar-mode growth rate in $D=6,7$. △ Less

Submitted 19 September, 2018; v1 submitted 3 July, 2018; originally announced July 2018.

Comments: 37 pages, 5 figures. v2: 39 pages, 5 figures. Improved discussion on black bars, and matching with previous numerics on bar-mode instabilities in D=6,7

Journal ref: JHEP 09 (2018) 107

Black holes, gravitational waves and fundamental physics: a roadmap

Authors: Leor Barack, Vitor Cardoso, Samaya Nissanke, Thomas P. Sotiriou, Abbas Askar, Krzysztof Belczynski, Gianfranco Bertone, Edi Bon, Diego Blas, Richard Brito, Tomasz Bulik, Clare Burrage, Christian T. Byrnes, Chiara Caprini, Masha Chernyakova, Piotr Chrusciel, Monica Colpi, Valeria Ferrari, Daniele Gaggero, Jonathan Gair, Juan Garcia-Bellido, S. F. Hassan, Lavinia Heisenberg, Martin Hendry, Ik Siong Heng , et al. (181 additional authors not shown)

Abstract: The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horiz… ▽ More The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress. △ Less

Submitted 1 February, 2019; v1 submitted 13 June, 2018; originally announced June 2018.

Comments: White Paper for the COST action "Gravitational Waves, Black Holes, and Fundamental Physics", 272 pages, 12 figures; v4: updated references and author list. Overall improvements and corrections. To appear in Classical and Quantum Gravity

Phases and Stability of Non-Uniform Black Strings

Authors: Roberto Emparan, Raimon Luna, Marina Martinez, Ryotaku Suzuki, Kentaro Tanabe

Abstract: We construct solutions of non-uniform black strings in dimensions from $D \approx 9$ all the way up to $D = \infty$, and investigate their thermodynamics and dynamical stability. Our approach employs the large-$D$ perturbative expansion beyond the leading order, including corrections up to $1/D^4$. Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out th… ▽ More We construct solutions of non-uniform black strings in dimensions from $D \approx 9$ all the way up to $D = \infty$, and investigate their thermodynamics and dynamical stability. Our approach employs the large-$D$ perturbative expansion beyond the leading order, including corrections up to $1/D^4$. Combining both analytical techniques and relatively simple numerical solution of ODEs, we map out the ranges of parameters in which non-uniform black strings exist in each dimension and compute their thermodynamics and quasinormal modes with accuracy. We establish with very good precision the existence of Sorkin's critical dimension and we prove that not only the thermodynamic stability, but also the dynamic stability of the solutions changes at it. △ Less

Submitted 1 May, 2020; v1 submitted 22 February, 2018; originally announced February 2018.

Comments: 39 pages, 32 figures. v2: Improved interpretation of the time evolution results. Added references and acknowledgments. 36 pages, 29 figures. v3: matches published version. v4: Corrected the large-D perturbative results in figs.5, 6, 7

Report number: AP-GR-143, OCU-PHYS-475

Journal ref: JHEP 05 (2018) 104

Black hole fusion in the extreme mass ratio limit

Authors: Roberto Emparan, Marina Martinez, Miguel Zilhao

Abstract: We present a simple, general, and accurate construction of the event horizons for the fusion of two neutral, rotating black holes with arbitrary orientation and values of their spins, in the extreme mass ratio limit where one black hole is much larger than the other. We compute several parameters that characterize the fusion and investigate their dependence on the black hole spin and orientation a… ▽ More We present a simple, general, and accurate construction of the event horizons for the fusion of two neutral, rotating black holes with arbitrary orientation and values of their spins, in the extreme mass ratio limit where one black hole is much larger than the other. We compute several parameters that characterize the fusion and investigate their dependence on the black hole spin and orientation axis. We also exhibit and study the appearance of transient toroidal topology of the horizon. An earlier conjecture about universal critical exponents before and after an axisymmetric pinch is proven. △ Less

Submitted 6 February, 2018; v1 submitted 29 August, 2017; originally announced August 2017.

Comments: 36 pages, 18 figures

Journal ref: Phys. Rev. D 97, 044004 (2018)

Geometric polarization of plasmas and Love numbers of AdS black branes

Authors: Roberto Emparan, Alejandro Fernandez-Pique, Raimon Luna

Abstract: We use AdS/CFT holography to study how a strongly-coupled plasma polarizes when the geometry where it resides is not flat. We compute the linear-response polarization coefficients, which are directly related to the static two-point correlation function of the stress-energy tensor. In the gravitational dual description, these parameters correspond to the tidal deformation coefficients---the Love nu… ▽ More We use AdS/CFT holography to study how a strongly-coupled plasma polarizes when the geometry where it resides is not flat. We compute the linear-response polarization coefficients, which are directly related to the static two-point correlation function of the stress-energy tensor. In the gravitational dual description, these parameters correspond to the tidal deformation coefficients---the Love numbers---of a black brane. We also compute the coefficients of static electric polarization of the plasma. △ Less

Submitted 29 September, 2017; v1 submitted 10 July, 2017; originally announced July 2017.

Comments: 23 pages, 9 figures. v2: Added references and acknowledgments. v3: Minor changes, references added (and retained). Matches published version

Journal ref: JHEP 09 (2017) 150

Exact Event Horizon of a Black Hole Merger

Authors: Roberto Emparan, Marina Martinez

Abstract: We argue that the event horizon of a binary black hole merger, in the extreme-mass-ratio limit where one of the black holes is much smaller than the other, can be described in an exact analytic way. This is done by tracing in the Schwarzschild geometry a congruence of null geodesics that approaches a null plane at infinity. Its form can be given explicitly in terms of elliptic functions, and we us… ▽ More We argue that the event horizon of a binary black hole merger, in the extreme-mass-ratio limit where one of the black holes is much smaller than the other, can be described in an exact analytic way. This is done by tracing in the Schwarzschild geometry a congruence of null geodesics that approaches a null plane at infinity. Its form can be given explicitly in terms of elliptic functions, and we use it to analyze and illustrate the time-evolution of the horizon along the merger. We identify features such as the line of caustics at which light rays enter the horizon, and the critical point at which the horizons touch. We also compute several quantities that characterize these aspects of the merger. △ Less

Submitted 27 June, 2016; v1 submitted 2 March, 2016; originally announced March 2016.

Comments: 21 pages, 17 figures. v2: Improved perturbative and critical analysis. Ancillary 3D animation of the merger. 24 pages, 18 figures. v3: minor improvements. 25 pages, 18 figures

Journal ref: Class.Quant.Grav. 33 (2016) 15, 155003

Hydro-elastic Complementarity in Black Branes at large D

Authors: Roberto Emparan, Keisuke Izumi, Raimon Luna, Ryotaku Suzuki, Kentaro Tanabe

Abstract: We obtain the effective theory for the non-linear dynamics of black branes---both neutral and charged, in asymptotically flat or Anti-deSitter spacetimes---to leading order in the inverse-dimensional expansion. We find that black branes evolve as viscous fluids, but when they settle down they are more naturally viewed as solutions of an elastic soap-bubble theory. The two views are complementary:… ▽ More We obtain the effective theory for the non-linear dynamics of black branes---both neutral and charged, in asymptotically flat or Anti-deSitter spacetimes---to leading order in the inverse-dimensional expansion. We find that black branes evolve as viscous fluids, but when they settle down they are more naturally viewed as solutions of an elastic soap-bubble theory. The two views are complementary: the same variable is regarded in one case as the energy density of the fluid, in the other as the deformation of the elastic membrane. The large-D theory captures finite-wavelength phenomena beyond the conventional reach of hydrodynamics. For asymptotically flat charged black branes (either Reissner-Nordstrom or p-brane-charged black branes) it yields the non-linear evolution of the Gregory-Laflamme instability at large D and its endpoint at stable non-uniform black branes. For Reissner-Nordstrom AdS black branes we find that sound perturbations do not propagate (have purely imaginary frequency) when their wavelength is below a certain charge-dependent value. We also study the polarization of black branes induced by an external electric field. △ Less

Submitted 27 June, 2016; v1 submitted 18 February, 2016; originally announced February 2016.

Comments: 26 pages. v2: 33 pages. Appendix added with a systematic derivation of the effective equations. v3: 34 pages. Expanded introduction

Report number: KEK-TH-1885, OCU-PHYS-438, AP-GR-130

Journal ref: JHEP 06 (2016) 117

Evolution and endpoint of the black string instability: Large D solution

Authors: Roberto Emparan, Ryotaku Suzuki, Kentaro Tanabe

Abstract: We derive a simple set of non-linear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and a… ▽ More We derive a simple set of non-linear, (1+1)-dimensional partial differential equations that describe the dynamical evolution of black strings and branes to leading order in the expansion in the inverse of the number of dimensions D. These equations are easily solved numerically. Their solution shows that thin enough black strings are unstable to developing inhomogeneities along their length, and at late times they asymptote to stable non-uniform black strings. This proves an earlier conjecture about the endpoint of the instability of black strings in a large enough number of dimensions. If the initial black string is very thin, the final configuration is highly non-uniform and resembles a periodic array of localized black holes joined by short necks. We also present the equations that describe the non-linear dynamics of Anti-deSitter black branes at large D. △ Less

Submitted 29 June, 2015; v1 submitted 22 June, 2015; originally announced June 2015.

Comments: 8 pages, 2 figures. v2: slightly more general equations and other small improvements

Report number: KEK-TH-1838, OCU-PHYS-429, AP-GR-126

Journal ref: Phys. Rev. Lett. 115, 091102 (2015)

Effective theory of Black Holes in the 1/D expansion

Authors: Roberto Emparan, Tetsuya Shiromizu, Ryotaku Suzuki, Kentaro Tanabe, Takahiro Tanaka

Abstract: The gravitational field of a black hole is strongly localized near its horizon when the number of dimensions D is very large. In this limit, we can effectively replace the black hole with a surface in a background geometry (eg Minkowski or Anti-deSitter space). The Einstein equations determine the effective equations that this 'black hole surface' (or membrane) must satisfy. We obtain them up to n… ▽ More The gravitational field of a black hole is strongly localized near its horizon when the number of dimensions D is very large. In this limit, we can effectively replace the black hole with a surface in a background geometry (eg Minkowski or Anti-deSitter space). The Einstein equations determine the effective equations that this 'black hole surface' (or membrane) must satisfy. We obtain them up to next-to-leading order in 1/D for static black holes of the Einstein-(A)dS theory. To leading order, and also to next order in Minkowski backgrounds, the equations of the effective theory are the same as soap-film equations, possibly up to a redshift factor. In particular, the Schwarzschild black hole is recovered as a spherical soap bubble. Less trivially, we find solutions for 'black droplets', ie black holes localized at the boundary of AdS, and for non-uniform black strings. △ Less

Submitted 24 April, 2015; originally announced April 2015.

Comments: 32 pages, 3 figures

Report number: KEK-TH-1810, AP-GR-122, OCU-PHYS-422, KUNS 2557, YITP-15-33

Journal ref: JHEP 06 (2015) 159

Quasinormal modes of (Anti-)de Sitter black holes in the 1/D expansion

Authors: Roberto Emparan, Ryotaku Suzuki, Kentaro Tanabe

Abstract: We use the inverse-dimensional expansion to compute analytically the frequencies of a set of quasinormal modes of static black holes of Einstein-(Anti-)de Sitter gravity, including the cases of spherical, planar or hyperbolic horizons. The modes we study are decoupled modes localized in the near-horizon region, which are the ones that capture physics peculiar to each black hole (such as their inst… ▽ More We use the inverse-dimensional expansion to compute analytically the frequencies of a set of quasinormal modes of static black holes of Einstein-(Anti-)de Sitter gravity, including the cases of spherical, planar or hyperbolic horizons. The modes we study are decoupled modes localized in the near-horizon region, which are the ones that capture physics peculiar to each black hole (such as their instabilities), and which in large black holes contain hydrodynamic behavior. Our results also give the unstable Gregory-Laflamme frequencies of Ricci-flat black branes to two orders higher in 1/D than previous calculations. We discuss the limits on the accuracy of these results due to the asymptotic but not convergent character of the 1/D expansion, which is due to the violation of the decoupling condition at finite D. Finally, we compare the frequencies for AdS black branes to calculations in the hydrodynamic expansion in powers of the momentum k. Our results extend up to k^9 for the sound mode and to k^8 for the shear mode. △ Less

Submitted 10 February, 2015; originally announced February 2015.

Comments: 20 pages, 3 figures

Report number: KEK-TH-1794, AP-GR-119, OCU-PHYS-419

Journal ref: JHEP 04 (2015) 085

Bumpy black holes

Authors: Roberto Emparan, Pau Figueras, Marina Martinez

Abstract: We study six-dimensional rotating black holes with bumpy horizons: these are topologically spherical, but the sizes of symmetric cycles on the horizon vary non-monotonically with the polar angle. We construct them numerically for the first three bumpy families, and follow them in solution space until they approach critical solutions with localized singularities on the horizon. We find strong evide… ▽ More We study six-dimensional rotating black holes with bumpy horizons: these are topologically spherical, but the sizes of symmetric cycles on the horizon vary non-monotonically with the polar angle. We construct them numerically for the first three bumpy families, and follow them in solution space until they approach critical solutions with localized singularities on the horizon. We find strong evidence of the conical structures that have been conjectured to mediate the transitions to black rings, to black Saturns, and to a novel class of bumpy black rings. For a different, recently identified class of bumpy black holes, we find evidence that this family ends in solutions with a localized singularity that exhibits apparently universal properties, and which does not seem to allow for transitions to any known class of black holes. △ Less

Submitted 11 December, 2014; v1 submitted 17 October, 2014; originally announced October 2014.

Comments: 24 pages, 33 figures. v2: published version

Journal ref: JHEP 1412 (2014) 072

Decoupling and non-decoupling dynamics of large D black holes

Authors: Roberto Emparan, Ryotaku Suzuki, Kentaro Tanabe

Abstract: The limit of large number of dimensions localizes the gravitational field of a black hole in a well-defined region near the horizon. The perturbative dynamics of the black hole can then be characterized in terms of states in the near-horizon geometry. We investigate this by computing the spectrum of quasinormal modes of the Schwarzschild black hole in the 1/D expansion, which we find splits into t… ▽ More The limit of large number of dimensions localizes the gravitational field of a black hole in a well-defined region near the horizon. The perturbative dynamics of the black hole can then be characterized in terms of states in the near-horizon geometry. We investigate this by computing the spectrum of quasinormal modes of the Schwarzschild black hole in the 1/D expansion, which we find splits into two classes. Most modes are non-decoupled modes: non-normalizable states of the near-horizon geometry that straddle between the near-horizon zone and the asymptotic zone. They have frequency of order D/r_0 (with r_0 the horizon radius), and are also present in a large class of other black holes. There also exist a much smaller number of decoupled modes: normalizable states of the near-horizon geometry that are strongly suppressed in the asymptotic region. They have frequency of order 1/r_0, and are specific of each black hole. Our results for their frequencies are in excellent agreement with numerical calculations, in some cases even in D=4. △ Less

Submitted 12 June, 2014; v1 submitted 4 June, 2014; originally announced June 2014.

Comments: 30 pages, 13 figures; v2: minor corrections

Report number: YITP-14-45, KEK-TH-1741

Journal ref: JHEP 07 (2014) 113

Instability of rotating black holes: large D analysis

Authors: Roberto Emparan, Ryotaku Suzuki, Kentaro Tanabe

Abstract: We study the stability of odd-dimensional rotating black holes with equal angular momenta by performing an expansion in the inverse of the number of dimensions D. Universality at large $D$ allows us to calculate analytically the complex frequency of quasinormal modes to next-to-leading order in the expansion. We identify the onset of non-axisymmetric, bar-mode instabilities at a specific finite ro… ▽ More We study the stability of odd-dimensional rotating black holes with equal angular momenta by performing an expansion in the inverse of the number of dimensions D. Universality at large $D$ allows us to calculate analytically the complex frequency of quasinormal modes to next-to-leading order in the expansion. We identify the onset of non-axisymmetric, bar-mode instabilities at a specific finite rotation, and axisymmetric instabilities at larger rotation. The former occur at the threshold where the modes become superradiant, and before the ultraspinning regime is reached. Our results fully confirm the picture found in numerical studies, with very good quantitative agreement. We extend the analysis to the same class of black holes in Anti-deSitter space, and find the same qualitative features. We also discuss the appearance at high frequencies of the universal set of (stable) quasinormal modes. △ Less

Submitted 15 May, 2014; v1 submitted 25 February, 2014; originally announced February 2014.

Comments: 38 pages, 14 figures. v3: NLO results included so the instability is shown to occur before the ultraspinning regime of rotation. Significant improvements in accuracy. Ancillary Mathematica notebook contains details of NLO results

Journal ref: JHEP 06 (2014) 106

Universal quasinormal modes of large D black holes

Authors: Roberto Emparan, Kentaro Tanabe

Abstract: We show that in the limit where the number of spacetime dimensions D grows to infinity a very large class of black holes (including non-extremal, static, asymptotically flat ones, with any number of gauge-field charges, possibly coupled to dilatons) possess a universal set of quasinormal modes whose complex frequencies depend only on the horizon radius and no other black hole parameters. The dampi… ▽ More We show that in the limit where the number of spacetime dimensions D grows to infinity a very large class of black holes (including non-extremal, static, asymptotically flat ones, with any number of gauge-field charges, possibly coupled to dilatons) possess a universal set of quasinormal modes whose complex frequencies depend only on the horizon radius and no other black hole parameters. The damping ratio of these modes vanishes like $D^{-2/3}$, so they are almost normal modes, or 'quasi-particle' excitations of the black hole. The structure responsible for the existence of these modes at large D is also present very generally in other black holes. △ Less

Submitted 9 January, 2014; originally announced January 2014.

Comments: 6 pages, 1 figure

Journal ref: Phys. Rev. D 89, 064028 (2014)

Holographic superconductivity in the large D expansion

Authors: Roberto Emparan, Kentaro Tanabe

Abstract: We study holographic superconductivity by expanding the equations in the inverse of the number of spacetime dimensions D. We obtain an analytic expression for the critical temperature as a function of the conformal dimension of the condensate operator. Its accuracy for 3+1-dimensional superconductors is better than 15%. The analysis reveals a simple, and quantitative, explanation for the onset of… ▽ More We study holographic superconductivity by expanding the equations in the inverse of the number of spacetime dimensions D. We obtain an analytic expression for the critical temperature as a function of the conformal dimension of the condensate operator. Its accuracy for 3+1-dimensional superconductors is better than 15%. The analysis reveals a simple, and quantitative, explanation for the onset of the superconducting instability, as well as universal features of holographic superconductivity in the large D limit. In particular, this allows to easily compute the effects of backreaction on the critical temperature. △ Less

Submitted 10 December, 2013; v1 submitted 4 December, 2013; originally announced December 2013.

Comments: 21 pages, 7 figures. v2: minor clarifications, refs added, lighter pdf file

Journal ref: JHEP 01 (2014) 145

Holographic collisions in confining theories

Authors: Vitor Cardoso, Roberto Emparan, David Mateos, Paolo Pani, Jorge V. Rocha

Abstract: We study the gravitational dual of a high-energy collision in a confining gauge theory. We consider a linearized approach in which two point particles traveling in an AdS-soliton background suddenly collide to form an object at rest (presumably a black hole for large enough center-of-mass energies). The resulting radiation exhibits the features expected in a theory with a mass gap: late-time power… ▽ More We study the gravitational dual of a high-energy collision in a confining gauge theory. We consider a linearized approach in which two point particles traveling in an AdS-soliton background suddenly collide to form an object at rest (presumably a black hole for large enough center-of-mass energies). The resulting radiation exhibits the features expected in a theory with a mass gap: late-time power law tails of the form t^(-3/2), the failure of Huygens' principle and distortion of the wave pattern as it propagates. The energy spectrum is exponentially suppressed for frequencies smaller than the gauge theory mass gap. Consequently, we observe no memory effect in the gravitational waveforms. At larger frequencies the spectrum has an upward-stairway structure, which corresponds to the excitation of the tower of massive states in the confining gauge theory. We discuss the importance of phenomenological cutoffs to regularize the divergent spectrum, and the aspects of the full non-linear collision that are expected to be captured by our approach. △ Less

Submitted 28 October, 2013; originally announced October 2013.

Comments: 65 pages, 18 figures

Journal ref: JHEP 01 (2014) 138

Black String Flow

Authors: Roberto Emparan, Marina Martinez

Abstract: We give an exact description of the steady flow of a black string into a planar horizon. The event horizon is out of equilibrium and provides a simple, exact instance of a `flowing black funnel' in any dimension D>=5. It is also an approximation to a smooth intersection between a black string and a black hole, in the limit in which the black hole is much larger than the black string thickness. The… ▽ More We give an exact description of the steady flow of a black string into a planar horizon. The event horizon is out of equilibrium and provides a simple, exact instance of a `flowing black funnel' in any dimension D>=5. It is also an approximation to a smooth intersection between a black string and a black hole, in the limit in which the black hole is much larger than the black string thickness. The construction extends easily to more general flows, in particular charged flows. △ Less

Submitted 8 July, 2013; originally announced July 2013.

Comments: 16 pages, 3 figures

Journal ref: JHEP 09 (2013) 068

Effective hydrodynamics of black D3-branes

Authors: Roberto Emparan, Veronika E Hubeny, Mukund Rangamani

Abstract: The long-wavelength effective field theory of world-volume fluctuations of black D3-branes is shown to be a hydrodynamical system to leading order in a gradient expansion. We study the system on a fiducial `cutoff' surface: the fluctuating geometry imprints its dynamics on the surface via an induced stress tensor whose conservation encapsulates the hydrodynamical description. For a generic non-ext… ▽ More The long-wavelength effective field theory of world-volume fluctuations of black D3-branes is shown to be a hydrodynamical system to leading order in a gradient expansion. We study the system on a fiducial `cutoff' surface: the fluctuating geometry imprints its dynamics on the surface via an induced stress tensor whose conservation encapsulates the hydrodynamical description. For a generic non-extremal D3-brane, as we move our cutoff surface from the asymptotically flat near-boundary region to the near-horizon region, this hydrodynamical system interpolates between a non-conformal relativistic fluid and a non-relativistic incompressible fluid. We also consider the dependence on the deviation from extremality of the D3-branes. In the near-extremal case we recover the description in terms of a conformal relativistic fluid encountered in the AdS/CFT context. We argue that this system allows us therefore to explore the various connections that have hitherto been suggested relating the dynamics of gravitational systems and fluid dynamics. In particular, we go on to show that the blackfold effective field theory approach allows us to capture this hydrodynamical behaviour and moreover subsumes the constructions encountered in the fluid/gravity correspondence and the black hole membrane paradigm, providing thereby a universal language to explore the effective dynamics of black branes. △ Less

Submitted 2 March, 2014; v1 submitted 14 March, 2013; originally announced March 2013.

Comments: 36 pages, 4 figures (pdf). v2: added refs. v3: typos fixed

Report number: DCPT-13/11

Journal ref: JHEP 06 (2013) 035

Large D gravity and low D strings

Authors: Roberto Emparan, Daniel Grumiller, Kentaro Tanabe

Abstract: We point out that in the limit of large number of dimensions a wide class of non-extremal neutral black holes has a universal near horizon limit. The limiting geometry is the two-dimensional black hole of string theory with a two-dimensional target space. Its conformal symmetry explains properties of massless scalars found recently in the large D limit. In analogy to the situation for NS fivebrane… ▽ More We point out that in the limit of large number of dimensions a wide class of non-extremal neutral black holes has a universal near horizon limit. The limiting geometry is the two-dimensional black hole of string theory with a two-dimensional target space. Its conformal symmetry explains properties of massless scalars found recently in the large D limit. In analogy to the situation for NS fivebranes, the dynamics near the horizon does not decouple from the asymptotically flat region. We generalize the discussion to charged black p-branes. For black branes with string charges, the near horizon geometry is that of the three-dimensional black strings of Horne and Horowitz. The analogies between the alpha' expansion in string theory and the large D expansion in gravity suggest a possible effective string description of the large D limit of black holes. We comment on applications to several subjects, in particular to the problem of critical collapse. △ Less

Submitted 20 March, 2013; v1 submitted 8 March, 2013; originally announced March 2013.

Comments: 10 pages. v2: ref. added, minor corrections

Report number: TUW-13-04

Journal ref: Phys. Rev. Lett. 110 (2013) 251102