pith. machine review for the scientific record. sign in

arxiv: 2510.04703 · v2 · submitted 2025-10-06 · 🌀 gr-qc · astro-ph.HE

Testing black hole metrics with binary black hole inspirals

Zhe Zhao , Swarnim Shashank , Debtroy Das , Cosimo Bambi This is my paper

Pith reviewed 2026-05-18 09:44 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords gravitational wavesKerr metricblack hole testsgeneral relativitybinary black hole inspiralseffective one-bodyparameterized post-Einsteinianno-hair theorem
0
0 comments X

The pith

Gravitational wave data from binary black hole inspirals show no significant deviations from the Kerr metric of general relativity.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper tests whether black holes follow the exact Kerr geometry of general relativity by examining the gravitational wave signals emitted during the inspiral phase of binary mergers. It introduces parameterized deviations from the Kerr solution and computes their impact on the waveform phase using the effective one-body approach together with the parameterized post-Einsteinian framework. Comparison with existing detector data finds consistency with zero deviation, confirming the Kerr description within present measurement precision. The analysis also shows that orbital eccentricity contributes only a subdominant effect. These results supply a direct observational route to checking the no-hair theorem in the strong-field regime.

Core claim

Using effective one-body waveforms and the parameterized post-Einsteinian framework to model deviations from the Kerr metric, the authors constrain the parameters of several well-motivated non-Kerr spacetimes and find that current gravitational wave observations from binary black hole inspirals are fully consistent with the Kerr solution, showing no significant deviations from general relativity and thereby supporting its validity within observational limits; orbital eccentricity remains subdominant in the allowed range.

What carries the argument

Parameterized post-Einsteinian framework applied to effective one-body gravitational wave phase calculations to bound metric deviations from Kerr.

If this is right

  • The no-hair theorem receives observational support for astrophysical black holes.
  • General relativity remains consistent with data in the strong-field regime near black hole horizons.
  • Eccentricity effects can be neglected at current precision without biasing the metric constraints.
  • The same modeling pipeline supplies a concrete method for testing additional modified black hole solutions with upcoming detections.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Any alternative gravity theory must reproduce Kerr-like waveforms to high accuracy at the frequencies and amplitudes already observed.
  • The framework can be extended to lower-frequency observations from space-based detectors to probe different regimes of potential deviations.
  • Similar phase constraints could be applied to other compact-object binaries once waveform models for those systems mature.

Load-bearing premise

The parameterized post-Einsteinian modifications combined with effective one-body waveforms fully capture the leading-order effects of the chosen metric deviations on the gravitational wave phase without significant unmodeled correlations or higher-order terms.

What would settle it

A future binary black hole inspiral detection whose measured gravitational wave phase shift matches one of the tested non-Kerr metrics at a statistically significant level while disagreeing with the Kerr prediction would falsify the no-deviation conclusion.

Figures

Figures reproduced from arXiv: 2510.04703 by Cosimo Bambi, Debtroy Das, Swarnim Shashank, Zhe Zhao.

Figure 1
Figure 1. Figure 1: Violin plots for the deformation parameters of the BH spacetimes beyond GR considered [PITH_FULL_IMAGE:figures/full_fig_p020_1.png] view at source ↗
read the original abstract

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

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript develops a pipeline to test specific deviations from the Kerr metric by generating binary black hole inspiral waveforms via the effective one-body (EOB) formalism and then mapping the resulting phase shifts into the parameterized post-Einsteinian (ppE) framework for parameter estimation against existing gravitational-wave observations. It reports that the data are consistent with the Kerr solution (no significant deviations detected) and that eccentricity is subdominant within observationally allowed ranges.

Significance. If the mapping from metric deviations to ppE parameters is shown to be complete at the relevant order, the work supplies a concrete route for converting theoretical non-Kerr solutions into falsifiable bounds using current LIGO/Virgo data and thereby contributes to strong-field tests of the no-hair theorem.

major comments (2)
  1. [§3] §3 (Waveform construction): The central claim that ppE parameters fully capture the phase effects of the chosen metric deviations rests on the unverified assumption that higher-order or metric-specific contributions (secular drifts, resonant effects) lie outside the ppE basis; without an explicit residual-phase comparison or injection-recovery test demonstrating that post-fit residuals remain below the statistical uncertainty of the data, the reported bounds on deviation parameters may be biased or incomplete.
  2. [§4] §4 (Results and constraints): The abstract and results state that 'no significant deviations' are found, yet the manuscript provides neither quantitative 90 % credible intervals on the deviation parameters, an error budget, nor the specific GW events and SNR thresholds employed; this omission prevents independent assessment of whether the null result is statistically meaningful or merely a consequence of limited sensitivity.
minor comments (2)
  1. [Abstract] The abstract refers to 'a series of well-motivated deviations' without naming the concrete metrics (e.g., Johannsen-Psaltis, bumpy Kerr, or others); listing them explicitly in the introduction would improve readability.
  2. [§2.2] Notation for the ppE parameters (e.g., β, γ) should be cross-referenced to the original Yunes et al. definitions to avoid ambiguity with other conventions in the literature.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their careful reading of the manuscript and for the constructive comments, which have helped us improve the clarity and rigor of the presentation. We address each major comment below and indicate the revisions made to the manuscript.

read point-by-point responses

  1. Referee: [§3] §3 (Waveform construction): The central claim that ppE parameters fully capture the phase effects of the chosen metric deviations rests on the unverified assumption that higher-order or metric-specific contributions (secular drifts, resonant effects) lie outside the ppE basis; without an explicit residual-phase comparison or injection-recovery test demonstrating that post-fit residuals remain below the statistical uncertainty of the data, the reported bounds on deviation parameters may be biased or incomplete.

    Authors: We agree that an explicit verification of the mapping completeness strengthens the analysis. The ppE parameterization is constructed to capture the leading-order phase deviations from general relativity at the post-Newtonian orders relevant to the inspiral regime considered here. To address the concern directly, the revised manuscript now includes a residual-phase comparison between the EOB waveforms with the chosen metric deviations and the corresponding ppE approximations after fitting. The residuals remain below the statistical uncertainty across the frequency band and SNR range of the observations. We have also added a short discussion explaining why secular drifts and resonant effects fall outside the relevant band for the events analyzed. revision: yes

  2. Referee: [§4] §4 (Results and constraints): The abstract and results state that 'no significant deviations' are found, yet the manuscript provides neither quantitative 90 % credible intervals on the deviation parameters, an error budget, nor the specific GW events and SNR thresholds employed; this omission prevents independent assessment of whether the null result is statistically meaningful or merely a consequence of limited sensitivity.

    Authors: We accept that the original presentation omitted key quantitative details needed for independent evaluation. The revised manuscript now includes a table reporting the 90% credible intervals on the deviation parameters for each event. We explicitly list the gravitational-wave events used (those with network SNR above 8) and provide an error budget that incorporates waveform modeling systematics and detector calibration uncertainties. These additions make the statistical significance of the null result transparent. revision: yes

Circularity Check

0 steps flagged

No circularity: constraints derived from external GW data fits using standard ppE+EOB methods

full rationale

The paper's derivation computes inspiral phases via the effective one-body formalism applied to chosen non-Kerr metrics, then maps leading deviations into the parameterized post-Einsteinian basis before performing parameter estimation against real LIGO/Virgo events. This chain relies on external observational data and established waveform models rather than any self-definitional loop, fitted input renamed as prediction, or load-bearing self-citation. The final claim that data support the Kerr hypothesis is therefore a direct statistical outcome of the fit and remains independent of the paper's own inputs.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

The analysis rests on standard assumptions in gravitational wave modeling and data analysis rather than new postulates.

free parameters (1)
  • deviation parameters
    Parameters quantifying possible deviations from the Kerr metric that are fitted to the gravitational wave data.
axioms (2)
  • domain assumption The effective one-body formalism accurately models the inspiral waveform phase for the considered non-Kerr metrics.
    Invoked to compute the gravitational wave phase used in the analysis.
  • domain assumption The parameterized post-Einsteinian framework captures the dominant effects of metric deviations on the waveform without missing important correlations.
    Central to the parameter estimation procedure described.

pith-pipeline@v0.9.0 · 5743 in / 1340 out tokens · 35031 ms · 2026-05-18T09:44:47.040343+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

74 extracted references · 74 canonical work pages · 37 internal anchors

  1. [1]

    R. M. Wald, Chicago Univ. Pr., 1984, doi:10.7208/chicago/9780226870373.001.0001

    work page doi:10.7208/chicago/9780226870373.001.0001 1984

  2. [2]

    Liang, B

    C. Liang, B. Zhou and W. Jia, Springer, 2023, ISBN 978-981-99-0021-3, 978-981-99-0024-4, 978- 981-99-0022-0 doi:10.1007/978-981-99-0022-0

    work page doi:10.1007/978-981-99-0022-0 2023

  3. [3]

    B. P. Abbottet al.[LIGO Scientific and Virgo], Phys. Rev. Lett.116(2016) no.6, 061102 doi:10.1103/PhysRevLett.116.061102 [arXiv:1602.03837 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.116.061102 2016

  4. [4]

    B. P. Abbottet al.[LIGO Scientific and Virgo], Phys. Rev. Lett.119(2017) no.16, 161101 doi:10.1103/PhysRevLett.119.161101 [arXiv:1710.05832 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.119.161101 2017

  5. [5]

    Blundell, Magnetism in Condensed Matter , Oxford University Press (10, 2001), 10.1093/oso/9780198505921.001.0001

    M. Maggiore, Oxford University Press, 2007, ISBN 978-0-19-171766-6, 978-0-19-852074-0 doi:10.1093/acprof:oso/9780198570745.001.0001

    work page doi:10.1093/acprof:oso/9780198570745.001.0001 2007

  6. [6]

    Perkins and N

    S. Perkins and N. Yunes, Phys. Rev. D105(2022) no.12, 124047 doi:10.1103/PhysRevD.105.124047 [arXiv:2201.02542 [gr-qc]]

    work page doi:10.1103/physrevd.105.124047 2022

  7. [7]

    Introductory lectures on the Effective One Body formalism

    T. Damour, Int. J. Mod. Phys. A23(2008), 1130-1148 doi:10.1142/S0217751X08039992 [arXiv:0802.4047 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0217751x08039992 2008

  8. [8]

    Post-Newtonian Theory for Gravitational Waves

    L. Blanchet, Living Rev. Rel.17(2014), 2 doi:10.12942/lrr-2014-2 [arXiv:1310.1528 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.12942/lrr-2014-2 2014

  9. [9]

    Effective one-body approach to general relativistic two-body dynamics

    A. Buonanno and T. Damour, Phys. Rev. D59(1999), 084006 doi:10.1103/PhysRevD.59.084006 [arXiv:gr-qc/9811091 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.59.084006 1999

  10. [10]

    Damour, Phys

    T. Damour, Phys. Rev. D64(2001), 124013 doi:10.1103/PhysRevD.64.124013 [arXiv:gr- qc/0103018 [gr-qc]]

    work page doi:10.1103/physrevd.64.124013 2001

  11. [11]

    R. S. Chandramouli, K. Prokup, E. Berti and N. Yunes, Phys. Rev. D111(2025) no.4, 044026 doi:10.1103/PhysRevD.111.044026 [arXiv:2410.06254 [gr-qc]]

    work page doi:10.1103/physrevd.111.044026 2025

  12. [12]

    Fundamental Theoretical Bias in Gravitational Wave Astrophysics and the Parameterized Post-Einsteinian Framework

    N. Yunes and F. Pretorius, Phys. Rev. D80(2009), 122003 doi:10.1103/PhysRevD.80.122003 [arXiv:0909.3328 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.80.122003 2009

  13. [13]

    Cardenas-Avendano, S

    A. Cardenas-Avendano, S. Nampalliwar and N. Yunes, Class. Quant. Grav.37(2020) no.13, 135008 doi:10.1088/1361-6382/ab8f64 [arXiv:1912.08062 [gr-qc]]

    work page doi:10.1088/1361-6382/ab8f64 2020

  14. [14]

    Shashank and C

    S. Shashank and C. Bambi, Phys. Rev. D105(2022) no.10, 104004 doi:10.1103/PhysRevD.105.104004 [arXiv:2112.05388 [gr-qc]]

    work page doi:10.1103/physrevd.105.104004 2022

  15. [15]

    D. Das, S. Shashank and C. Bambi, Eur. Phys. J. C84, no.11, 1237 (2024) doi:10.1140/epjc/s10052- 024-13623-7 [arXiv:2406.03846 [gr-qc]]

    work page doi:10.1140/epjc/s10052- 2024

  16. [16]

    P. A. Seoaneet al.[LISA], Living Rev. Rel.26(2023) no.1, 2 doi:10.1007/s41114-022-00041-y [arXiv:2203.06016 [gr-qc]]

    work page doi:10.1007/s41114-022-00041-y 2023

  17. [17]

    Blanchet, Living Rev

    L. Blanchet, Living Rev. Rel.9(2006), 4

    work page 2006

  18. [18]

    Foundations of an effective-one-body model for coalescing binaries on eccentric orbits

    T. Hinderer and S. Babak, Phys. Rev. D96(2017) no.10, 104048 doi:10.1103/PhysRevD.96.104048 [arXiv:1707.08426 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.96.104048 2017

  19. [19]

    S. Khan, S. Husa, M. Hannam, F. Ohme, M. P¨ urrer, X. Jim´ enez Forteza and A. Boh´ e, Phys. Rev. D93(2016) no.4, 044007 doi:10.1103/PhysRevD.93.044007 [arXiv:1508.07253 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.93.044007 2016

  20. [20]

    P. K. Gupta, T. F. M. Spieksma, P. T. H. Pang, G. Koekoek and C. V. Broeck, Phys. Rev. D104, no.6, 063041 (2021) doi:10.1103/PhysRevD.104.063041 [arXiv:2107.12111 [gr-qc]]

    work page doi:10.1103/physrevd.104.063041 2021

  21. [21]

    R. P. Kerr, Phys. Rev. Lett.11(1963), 237-238 doi:10.1103/PhysRevLett.11.237 22

    work page doi:10.1103/physrevlett.11.237 1963

  22. [22]

    E. T. Newman and A. I. Janis, J. Math. Phys.6(1965), 915-917 doi:10.1063/1.1704350

    work page doi:10.1063/1.1704350 1965

  23. [23]

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

    S. Vagnozzi, R. Roy, Y. D. Tsai, L. Visinelli, M. Afrin, A. Allahyari, P. Bambhaniya, D. Dey, S. G. Ghosh and P. S. Joshi,et al.Class. Quant. Grav.40(2023) no.16, 165007 doi:10.1088/1361- 6382/acd97b [arXiv:2205.07787 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/1361- 2023

  24. [24]

    Apparent shape of super-spinning black holes

    C. Bambi and K. Freese, Phys. Rev. D79, 043002 (2009) doi:10.1103/PhysRevD.79.043002 [arXiv:0812.1328 [astro-ph]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.79.043002 2009

  25. [25]

    Testing the Kerr black hole hypothesis using X-ray reflection spectroscopy

    C. Bambi, A. Cardenas-Avendano, T. Dauser, J. A. Garcia and S. Nampalliwar, Astrophys. J.842 (2017) no.2, 76 doi:10.3847/1538-4357/aa74c0 [arXiv:1607.00596 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/aa74c0 2017

  26. [26]

    A. B. Abdikamalov, D. Ayzenberg, C. Bambi, T. Dauser, J. A. Garcia and S. Nampalliwar, Astro- phys. J.878(2019) no.2, 91 doi:10.3847/1538-4357/ab1f89 [arXiv:1902.09665 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab1f89 2019

  27. [27]

    A. B. Abdikamalov, D. Ayzenberg, C. Bambi, T. Dauser, J. A. Garcia, S. Nampalliwar, A. Tripathi and M. Zhou, Astrophys. J.899, no.1, 80 (2020) doi:10.3847/1538-4357/aba625 [arXiv:2003.09663 [astro-ph.HE]]

    work page doi:10.3847/1538-4357/aba625 2020

  28. [28]

    Testing black hole candidates with electromagnetic radiation

    C. Bambi, Rev. Mod. Phys.89(2017) no.2, 025001 doi:10.1103/RevModPhys.89.025001 [arXiv:1509.03884 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/revmodphys.89.025001 2017

  29. [29]

    Z. Cao, S. Nampalliwar, C. Bambi, T. Dauser and J. A. Garcia, Phys. Rev. Lett.120(2018) no.5, 051101 doi:10.1103/PhysRevLett.120.051101 [arXiv:1709.00219 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevlett.120.051101 2018

  30. [30]

    Constraints on the spacetime metric around seven "bare" AGNs using X-ray reflection spectroscopy

    A. Tripathi, J. Yan, Y. Yang, Y. Yan, M. Garnham, Y. Yao, S. Li, Z. Ding, A. B. Abdika- malov and D. Ayzenberg,et al.Astrophys. J.874(2019) no.2, 135 doi:10.3847/1538-4357/ab0a00 [arXiv:1901.03064 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab0a00 2019

  31. [31]

    Towards precision tests of general relativity with black hole X-ray reflection spectroscopy

    A. Tripathi, S. Nampalliwar, A. B. Abdikamalov, D. Ayzenberg, C. Bambi, T. Dauser, J. A. Garcia and A. Marinucci, Astrophys. J.875, no.1, 56 (2019) doi:10.3847/1538-4357/ab0e7e [arXiv:1811.08148 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/1538-4357/ab0e7e 2019

  32. [32]

    Tripathi, Y

    A. Tripathi, Y. Zhang, A. B. Abdikamalov, D. Ayzenberg, C. Bambi, J. Jiang, H. Liu and M. Zhou, Astrophys. J.913, no.2, 79 (2021) doi:10.3847/1538-4357/abf6cd [arXiv:2012.10669 [astro-ph.HE]]

    work page doi:10.3847/1538-4357/abf6cd 2021

  33. [33]

    Bardeen, J. 1968. Non-singular general relativistic gravitational collapse. Proceedings of the 5th International Conference on Gravitation and the Theory of Relativity, 87

    work page 1968

  34. [34]

    The Bardeen Model as a Nonlinear Magnetic Monopole

    E. Ayon-Beato and A. Garcia, Phys. Lett. B493(2000), 149-152 doi:10.1016/S0370-2693(00)01125- 4 [arXiv:gr-qc/0009077 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0370-2693(00)01125- 2000

  35. [35]

    Four Parametric Regular Black Hole Solution

    E. Ayon-Beato and A. Garcia, Gen. Rel. Grav.37(2005), 635 doi:10.1007/s10714-005-0050-y [arXiv:hep-th/0403229 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s10714-005-0050-y 2005

  36. [36]

    R. V. Maluf and J. C. S. Neves, Int. J. Mod. Phys. D28(2018) no.03, 1950048 doi:10.1142/S0218271819500482 [arXiv:1801.08872 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1142/s0218271819500482 2018

  37. [37]

    Rotating regular black holes

    C. Bambi and L. Modesto, Phys. Lett. B721(2013), 329-334 doi:10.1016/j.physletb.2013.03.025 [arXiv:1302.6075 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2013.03.025 2013

  38. [38]

    Testing the Bardeen metric with the black hole candidate in Cygnus X-1

    C. Bambi, Phys. Lett. B730(2014), 59-62 doi:10.1016/j.physletb.2014.01.037 [arXiv:1401.4640 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.physletb.2014.01.037 2014

  39. [39]

    S. A. Hayward, Phys. Rev. Lett.96(2006), 031103 doi:10.1103/PhysRevLett.96.031103 [arXiv:gr- qc/0506126 [gr-qc]]

    work page doi:10.1103/physrevlett.96.031103 2006

  40. [40]

    Renormalization group improved black hole spacetimes

    A. Bonanno and M. Reuter, Phys. Rev. D62(2000), 043008 doi:10.1103/PhysRevD.62.043008 [arXiv:hep-th/0002196 [hep-th]]. 23

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.62.043008 2000

  41. [41]

    Non-singular quantum improved rotating black holes and their maximal extension

    R. Torres, Gen. Rel. Grav.49(2017) no.6, 74 doi:10.1007/s10714-017-2236-5 [arXiv:1702.03567 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s10714-017-2236-5 2017

  42. [42]

    B. Zhou, A. B. Abdikamalov, D. Ayzenberg, C. Bambi, S. Nampalliwar and A. Tripathi, JCAP01 (2021), 047 doi:10.1088/1475-7516/2021/01/047 [arXiv:2005.12958 [astro-ph.HE]]

    work page doi:10.1088/1475-7516/2021/01/047 2021

  43. [43]

    Bodendorfer, F

    N. Bodendorfer, F. M. Mele and J. M¨ unch, Phys. Lett. B819(2021), 136390 doi:10.1016/j.physletb.2021.136390 [arXiv:1911.12646 [gr-qc]]

    work page doi:10.1016/j.physletb.2021.136390 2021

  44. [44]

    Bodendorfer, F

    N. Bodendorfer, F. M. Mele and J. M¨ unch, Class. Quant. Grav.38(2021) no.9, 095002 doi:10.1088/1361-6382/abe05d [arXiv:1912.00774 [gr-qc]]

    work page doi:10.1088/1361-6382/abe05d 2021

  45. [45]

    Brahma, C

    S. Brahma, C. Y. Chen and D. h. Yeom, Phys. Rev. Lett.126(2021) no.18, 181301 doi:10.1103/PhysRevLett.126.181301 [arXiv:2012.08785 [gr-qc]]

    work page doi:10.1103/physrevlett.126.181301 2021

  46. [46]

    Afrin, S

    M. Afrin, S. Vagnozzi and S. G. Ghosh, Astrophys. J.944(2023) no.2, 149 doi:10.3847/1538- 4357/acb334 [arXiv:2209.12584 [gr-qc]]

    work page doi:10.3847/1538- 2023

  47. [47]

    Hawking Radiation as Quantum Tunneling from Noncommutative Schwarzschild Black Hole

    K. Nozari and S. H. Mehdipour, Class. Quant. Grav.25(2008), 175015 doi:10.1088/0264- 9381/25/17/175015 [arXiv:0801.4074 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0264- 2008

  48. [48]

    M. A. Anacleto, F. A. Brito, J. A. V. Campos and E. Passos, Phys. Lett. B803(2020), 135334 doi:10.1016/j.physletb.2020.135334 [arXiv:1907.13107 [hep-th]]

    work page doi:10.1016/j.physletb.2020.135334 2020

  49. [49]

    A. A. Ara´ ujo Filho, J. R. Nascimento, A. Y. Petrov, P. J. Porf´ ırio and A.¨Ovg¨ un, Phys. Dark Univ. 47(2025), 101796 doi:10.1016/j.dark.2024.101796 [arXiv:2411.04674 [gr-qc]]

    work page doi:10.1016/j.dark.2024.101796 2025

  50. [50]

    Quantum corrections to gravity

    Y. Tomozawa, [arXiv:1107.1424 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv

  51. [51]

    Kumar and S

    R. Kumar and S. G. Ghosh, JCAP07(2020), 053 doi:10.1088/1475-7516/2020/07/053 [arXiv:2003.08927 [gr-qc]]

    work page doi:10.1088/1475-7516/2020/07/053 2020

  52. [52]

    D. J. Gross, J. A. Harvey, E. J. Martinec and R. Rohm, Phys. Rev. Lett.54(1985), 502-505 doi:10.1103/PhysRevLett.54.502

    work page doi:10.1103/physrevlett.54.502 1985

  53. [53]

    Sen, Phys

    A. Sen, Phys. Rev. Lett.69(1992), 1006-1009 doi:10.1103/PhysRevLett.69.1006 [arXiv:hep- th/9204046 [hep-th]]

    work page doi:10.1103/physrevlett.69.1006 1992

  54. [54]

    Yazadjiev, Gen

    S. Yazadjiev, Gen. Rel. Grav.32(2000), 2345-2352 doi:10.1023/A:1002080003862 [arXiv:gr- qc/9907092 [gr-qc]]

    work page doi:10.1023/a:1002080003862 2000

  55. [55]

    Tripathi, B

    A. Tripathi, B. Zhou, A. B. Abdikamalov, D. Ayzenberg and C. Bambi, JCAP07(2021), 002 doi:10.1088/1475-7516/2021/07/002 [arXiv:2103.07593 [astro-ph.HE]]

    work page doi:10.1088/1475-7516/2021/07/002 2021

  56. [56]

    S. G. Ghosh and R. K. walia, Annals Phys.434(2021), 168619 doi:10.1016/j.aop.2021.168619 [arXiv:2109.13031 [gr-qc]]

    work page doi:10.1016/j.aop.2021.168619 2021

  57. [57]

    D. I. Kazakov and S. N. Solodukhin, Nucl. Phys. B429(1994), 153-176 doi:10.1016/S0550- 3213(94)80045-6 [arXiv:hep-th/9310150 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0550- 1994

  58. [58]

    Kocherlakota and L

    P. Kocherlakota and L. Rezzolla, Phys. Rev. D102(2020) no.6, 064058 doi:10.1103/PhysRevD.102.064058 [arXiv:2007.15593 [gr-qc]]

    work page doi:10.1103/physrevd.102.064058 2020

  59. [59]

    Xu and M

    Z. Xu and M. Tang, Eur. Phys. J. C81(2021) no.10, 863 doi:10.1140/epjc/s10052-021-09635-2 [arXiv:2109.13813 [gr-qc]]

    work page doi:10.1140/epjc/s10052-021-09635-2 2021

  60. [60]

    Jusufi, M

    K. Jusufi, M. Azreg-A¨ ınou, M. Jamil and Q. Wu, Universe8(2022) no.4, 210 doi:10.3390/universe8040210 [arXiv:2203.14969 [gr-qc]]. 24

    work page doi:10.3390/universe8040210 2022

  61. [61]

    Regular black holes with a nonlinear electrodynamics source

    L. Balart and E. C. Vagenas, Phys. Rev. D90(2014) no.12, 124045 doi:10.1103/PhysRevD.90.124045 [arXiv:1408.0306 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevd.90.124045 2014

  62. [62]

    On a regular charged black hole with a nonlinear electric source

    H. Culetu, Int. J. Theor. Phys.54(2015) no.8, 2855-2863 doi:10.1007/s10773-015-2521-6 [arXiv:1408.3334 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1007/s10773-015-2521-6 2015

  63. [63]

    S. G. Ghosh, Eur. Phys. J. C75(2015) no.11, 532 doi:10.1140/epjc/s10052-015-3740-y [arXiv:1408.5668 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-015-3740-y 2015

  64. [64]

    V. K. Tinchev, Chin. J. Phys.53(2015), 110113 doi:10.6122/CJP.20150810 [arXiv:1512.09164 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.6122/cjp.20150810 2015

  65. [65]

    Hoffmann, Phys

    B. Hoffmann, Phys. Rev.47(1935) no.11, 877-880 doi:10.1103/PhysRev.47.877

    work page doi:10.1103/physrev.47.877 1935

  66. [67]

    G. W. Gibbons and D. A. Rasheed, Nucl. Phys. B476(1996), 515-547 doi:10.1016/0550- 3213(96)00365-3 [arXiv:hep-th/9604177 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/0550- 1996

  67. [68]

    Chruscinski, Phys

    D. Chruscinski, Phys. Rev. D62(2000), 105007 doi:10.1103/PhysRevD.62.105007 [arXiv:hep- th/0005215 [hep-th]]

    work page doi:10.1103/physrevd.62.105007 2000

  68. [69]

    D. P. Sorokin, [arXiv:hep-th/9709190 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv

  69. [70]

    D. J. Cirilo Lombardo, Class. Quant. Grav.21(2004), 1407-1417 doi:10.1088/0264-9381/21/6/009 [arXiv:gr-qc/0612063 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1088/0264-9381/21/6/009 2004

  70. [71]

    Horizon structure of rotating Einstein-Born-Infeld black holes and shadow

    F. Atamurotov, S. G. Ghosh and B. Ahmedov, Eur. Phys. J. C76(2016) no.5, 273 doi:10.1140/epjc/s10052-016-4122-9 [arXiv:1506.03690 [gr-qc]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1140/epjc/s10052-016-4122-9 2016

  71. [72]

    New Regular Black Hole Solution from Nonlinear Electrodynamics

    E. Ayon-Beato and A. Garcia, Phys. Lett. B464(1999), 25 doi:10.1016/S0370-2693(99)01038-2 [arXiv:hep-th/9911174 [hep-th]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/s0370-2693(99)01038-2 1999

  72. [73]

    Tests of general relativity with binary black holes from the second ligo–virgo gravitational- wave transient catalog - full posterior sample data release,

    LIGO Scientific Collaboration and Virgo Collaboration, “Tests of general relativity with binary black holes from the second ligo–virgo gravitational- wave transient catalog - full posterior sample data release,” (2021). doi: 10.7935/903s-gx73

    work page doi:10.7935/903s-gx73 2021

  73. [74]

    B. P. Abbottet al.[LIGO Scientific and Virgo], Phys. Rev. X9(2019) no.3, 031040 doi:10.1103/PhysRevX.9.031040 [arXiv:1811.12907 [astro-ph.HE]]

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.1103/physrevx.9.031040 2019

  74. [75]

    B. P. Abbottet al.[LIGO Scientific and Virgo], Astrophys. J. Lett.851(2017), L35 doi:10.3847/2041-8213/aa9f0c [arXiv:1711.05578 [astro-ph.HE]]. 25

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.3847/2041-8213/aa9f0c 2017