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Modified Teukolsky formalism: Null testing and numerical benchmarking
Authors:
Fawzi Aly,
Mahmoud A. Mansour,
Luis Lehner,
Dejan Stojkovic,
Dongjun Li,
Pratik Wagle
Abstract:
Next-generation gravitational-wave detectors will make black-hole ringdown an increasingly sensitive probe of small departures from General Relativity in the strong-field regime. This motivates obtaining high-precision predictions of gravitational effective field theory, as spectral shifts can be quite small. Here we perform a focused stress test of the modified-Teukolsky framework by designing tw…
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Next-generation gravitational-wave detectors will make black-hole ringdown an increasingly sensitive probe of small departures from General Relativity in the strong-field regime. This motivates obtaining high-precision predictions of gravitational effective field theory, as spectral shifts can be quite small. Here we perform a focused stress test of the modified-Teukolsky framework by designing two null diagnostics. First, we consider an action with redundant operators that must produce zero first-order vacuum QNM shifts. Second, we exploit a Ricci-flat identity relating two physical cubic Riemann to test such a relation is satisfied by the ringdown spectra obtained. We compute the shifts using two independent numerical approaches: the eigenvalue-perturbation and generalized continued-fraction (Leaver-type) methods. Both null tests are passed across multiple multipoles and overtones, and the control-operator results agree in magnitude with the benchmark values reported in Ref. [1]. These validations support using the framework for obtaining accurate predictions for robust strong-field tests, with straightforward extensions to rotating backgrounds and coupling with matter fields.
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Submitted 10 March, 2026; v1 submitted 2 March, 2026;
originally announced March 2026.
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More Nonlinearities? II. A Short Guide of First- and Second-Order Electromagnetic Perturbations in the Schwarzschild Background
Authors:
Fawzi Aly,
Mahmoud A. Mansour,
Dejan Stojkovic
Abstract:
We study second-order electromagnetic perturbations in the Schwarzschild background and derive the effective source terms for Regge-Wheeler equation which are quadratic in first-order gravitational and electromagnetic perturbations. In addition to the induced mixed quadratic modes, we find that linear gravitational modes are also excited, with amplitudes dependent on the electromagnetic potential.…
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We study second-order electromagnetic perturbations in the Schwarzschild background and derive the effective source terms for Regge-Wheeler equation which are quadratic in first-order gravitational and electromagnetic perturbations. In addition to the induced mixed quadratic modes, we find that linear gravitational modes are also excited, with amplitudes dependent on the electromagnetic potential. A toy model involving a Dirac delta function potential demonstrates mixing of linear gravitational and electromagnetic perturbations with frequencies \( ω^{(1)} \) and \( Ω^{(1)} \), resulting in the second-order QNM mixing in the electromagnetic field at \( Ω^{(2)} =Ω^{(1)} + ω^{(1)} \). This complements prior work in \cite{aly2024nonlinearities} on the second-order gravitational perturbation mixing and highlights potential applications in multi-messenger astrophysics for systems observed by LIGO-Virgo-KAGRA (LVK) and upcoming LISA. We also study first-order perturbations due to a point charge and show it could be reduced to a one-dimensional path integral. Within the toy model, we investigate the first-order electromagnetic perturbation due to a radially free-falling single charge \( q \) and radial dipole moment \( p = q η\), employing semi-analytical and numerical methods. For the dipole case, we show that the QNM perturbation is excited with a nearly constant amplitude. Future work will focus on incorporating mixing in more realistic potentials and exploring numerical approach in the context of rotating spacetimes.
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Submitted 18 November, 2025; v1 submitted 3 November, 2024;
originally announced November 2024.
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More Nonlinearities? Electromagnetic and Gravitational Mode Mixing in NSBH Mergers
Authors:
Fawzi Aly,
Mahmoud A. Mansour,
Dejan Stojkovic
Abstract:
We investigate the possibility of electromagnetic fields leaving imprints on gravitational wave (GW) signals from Neutron Star-Black hole (NSBH) mergers, specifically in the context of extreme mass ratio inspirals (EMRIs). Using black hole perturbation theory (BHPT) in the context of a minimally coupled Einstein-Maxwell system, we demonstrate that electromagnetic quasi normal modes(QNMs) can excit…
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We investigate the possibility of electromagnetic fields leaving imprints on gravitational wave (GW) signals from Neutron Star-Black hole (NSBH) mergers, specifically in the context of extreme mass ratio inspirals (EMRIs). Using black hole perturbation theory (BHPT) in the context of a minimally coupled Einstein-Maxwell system, we demonstrate that electromagnetic quasi normal modes(QNMs) can excite gravitational QNMs with frequencies that are linear or quadratic in the electromagnetic QNMs, at first level of mixing. Moreover, We then study the electromagnetism-gravity coupling by approximating the Regge-Wheeler and Zerilli potentials with Dirac delta functions. In this example, we examine gravitational perturbations induced by the electromagnetic field of an ideal dipole radially free fall towards the blackhole, building on calculations from a companion paper [1]. Our results show that both linear and quadratic electromagnetic QNMs appear in gravitational perturbations. In addition, linear gravitational QNMs are also excited due to the electromagnetic source, with their amplitudes depending on the details of the electromagnetic and gravitational potentials, analogous to gravitational mode mixing analysis. Furthermore, at late stages, gravitational perturbations might exhibit polynomial tails induced by electromagnetic perturbations. This article sets the stage for future numerical investigations aimed at identifying such modes in various scenarios.
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Submitted 5 November, 2024; v1 submitted 16 October, 2024;
originally announced October 2024.