pith. sign in

arxiv: 2606.24258 · v1 · pith:ACXLFVQHnew · submitted 2026-06-23 · 🌀 gr-qc · astro-ph.HE

Low-mass X-ray binaries as a probe of Kerr-MOG black hole spacetime

Bakhodirkhon Saidov , Bakhtiyor Narzilloev , Ibrar Hussain , Bobomurat Ahmedov This is my paper

Pith reviewed 2026-06-25 23:06 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HE
keywords Kerr-MOG spacetimelow-mass X-ray binariesradiative efficiencyjet powerBlandford-ZnajekISCOblack hole spin
0
0 comments X

The pith

Kerr-MOG black holes reproduce observed radiative efficiencies and jet powers in several low-mass X-ray binaries

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

The paper tests whether the Kerr-MOG spacetime, which adds a modified gravity parameter alpha to the usual mass and spin, can account for the properties of accretion disks and jets in stellar-mass black hole systems. Within the Novikov-Thorne model the extra parameter shifts the innermost stable orbit and therefore changes the fraction of gravitational energy converted to radiation. The authors derive allowed ranges of spin and alpha from measured efficiencies in six sources and then overlay the additional requirement that the predicted jet power match observed values. Overlap regions appear for most binaries, indicating that a single set of Kerr-MOG parameters can satisfy both observables at once.

Core claim

The presence of the MOG parameter alpha modifies the spacetime structure and the location of the ISCO. This affects the radiative efficiency of accretion disks and introduces a degeneracy between the spin and the modified gravity parameter. Using observational estimates and comparing with jet power predictions from the Blandford-Znajek mechanism, regions in the (a, alpha) space are identified where both observables are simultaneously reproduced for several sources, with only a narrow range for GRS1915+105.

What carries the argument

The Kerr-MOG geometry characterized by mass, spin parameter a, and modified gravity parameter alpha, which determines the ISCO location and thereby controls radiative efficiency and jet power.

If this is right

  • Alpha creates a degeneracy with spin in efficiency constraints.
  • Significant overlap regions in (a, alpha) exist for several sources when both efficiency and jet power are considered.
  • For the high-spin source GRS1915+105 compatibility requires only a narrow range of Kerr-MOG parameters.
  • The Kerr-MOG spacetime offers a viable framework for interpreting LMXB observations.

Where Pith is reading between the lines

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

  • New spin measurements with smaller uncertainties could tighten or exclude the allowed alpha intervals.
  • The same parameter constraints might be applied to other classes of black hole systems such as supermassive ones in active galaxies.
  • If alpha must be non-zero to fit the data, it would constitute evidence for modified gravity at stellar-mass scales.

Load-bearing premise

The Novikov-Thorne thin accretion disk model remains valid and the radiative efficiency is determined solely by the ISCO location even in Kerr-MOG spacetime.

What would settle it

Observational data on radiative efficiency or jet power for GRS1915+105 lying outside the narrow compatible interval in the (a, alpha) plane would falsify the model for that source.

Figures

Figures reproduced from arXiv: 2606.24258 by Bakhodirkhon Saidov, Bakhtiyor Narzilloev, Bobomurat Ahmedov, Ibrar Hussain.

Figure 1
Figure 1. Figure 1: FIG. 1. Variation of the horizon radii as functions of the spin parameter [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Allowed domain of the parameters ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. The ISCO radius of test particles as a function of the spin parameter [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. The radiative efficiency [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Variation of the horizon angular velocity [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Constraints on the spin parameter [PITH_FULL_IMAGE:figures/full_fig_p010_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. XTE J1550-564. The behavior observed in these diagrams is consistent with that of the previous case; a precise [PITH_FULL_IMAGE:figures/full_fig_p011_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: FIG. 8. GRS 1124-683. The left panel demonstrates that, for a Lorentz factor [PITH_FULL_IMAGE:figures/full_fig_p012_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. GRO J1655-40.The left panel corresponds to a Lorentz factor of [PITH_FULL_IMAGE:figures/full_fig_p012_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. For GRS 1915+105, the left and right panels show that the parameter regions consistent with the observed radiative [PITH_FULL_IMAGE:figures/full_fig_p014_10.png] view at source ↗
read the original abstract

We investigate the astrophysical implications of rotating black holes in modified gravity by studying the Kerr-MOG spacetime and applying it to several stellar-mass black hole candidates: A0620-00, H1743-322, XTE J1550-564, GRS1124-683, GRO J1655-40, and GRS1915+105. The Kerr-MOG geometry is characterized by the black hole mass, the spin parameter $a$, and the modified gravity parameter $\alpha$. We analyze how the presence of the MOG parameter modifies the spacetime structure and the location of the innermost stable circular orbit (ISCO). Within the Novikov--Thorne accretion disk model, we show that $\alpha$ significantly affects the radiative efficiency of accretion disks and introduces a degeneracy between the spin and the modified gravity parameter. Using observational estimates of radiative efficiencies inferred from the continuum-fitting method, we constrain the allowed regions in the $(a,\alpha)$ parameter space for each source. We further examine the relativistic jet power using the Blandford--Znajek mechanism and compare the theoretical predictions with the observed transient jet energetics, considering two representative jet Lorentz factors, $\Gamma=2$ and $\Gamma=5$. By combining the constraints from the radiative efficiency and jet power, we identify regions where both observables can be simultaneously reproduced. For several sources significant overlap regions appear, while for the highly spinning source GRS1915+105 the compatibility occurs only within a narrow range of Kerr--MOG parameters. These results suggest that the Kerr--MOG spacetime can provide a viable framework for interpreting the observed properties of several black hole X-ray binaries.

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 examines Kerr-MOG black holes applied to several low-mass X-ray binaries. It computes the ISCO location in the Kerr-MOG metric, applies the Novikov-Thorne thin-disk model to obtain radiative efficiencies as a function of spin a and MOG parameter α, and compares these to continuum-fitting observations to delineate allowed (a, α) regions. It further computes jet powers via the Blandford-Znajek mechanism for Lorentz factors Γ=2 and Γ=5, identifies overlap regions consistent with both efficiency and jet data, and notes a narrow compatible interval for the high-spin source GRS1915+105.

Significance. If the central mapping holds, the work supplies astrophysical constraints on the MOG parameter α from X-ray binary data and quantifies the spin-α degeneracy, thereby extending tests of modified gravity to stellar-mass black holes through accretion-disk and jet observables.

major comments (2)
  1. [Abstract and Novikov-Thorne section] Abstract (Novikov-Thorne application paragraph) and the corresponding methods section: radiative efficiencies are obtained by substituting the Kerr-MOG ISCO radius into the standard Novikov-Thorne binding-energy formula. The Kerr-MOG metric alters geodesic constants of motion and the effective potential, so the disk stress-energy tensor, vertical structure, and local energy flux require re-derivation from the modified Einstein equations rather than direct substitution of the new ISCO into the GR formula. This assumption is load-bearing for the efficiency constraints and the reported overlap regions, especially the narrow interval claimed for GRS1915+105.
  2. [Combined constraints section] Section on combined constraints (radiative efficiency plus jet power): the overlap regions are constructed by requiring the model to reproduce the same observational efficiency and jet-power numbers used to define the input constraints. No error budgets, robustness tests against model variations, or explicit propagation of observational uncertainties are supplied, so the claimed viable regions rest on unexamined assumptions about data and model fidelity.
minor comments (2)
  1. [Introduction] The definition and normalization of the MOG parameter α should be restated with an explicit reference to the original MOG field equations when first introduced.
  2. [Figures] The (a, α) contour plots would be clearer if observational error bars on efficiency and jet power were shown as shaded bands rather than point values.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments. Below we respond point-by-point to the major comments and indicate the revisions we will make.

read point-by-point responses

  1. Referee: [Abstract and Novikov-Thorne section] Abstract (Novikov-Thorne application paragraph) and the corresponding methods section: radiative efficiencies are obtained by substituting the Kerr-MOG ISCO radius into the standard Novikov-Thorne binding-energy formula. The Kerr-MOG metric alters geodesic constants of motion and the effective potential, so the disk stress-energy tensor, vertical structure, and local energy flux require re-derivation from the modified Einstein equations rather than direct substitution of the new ISCO into the GR formula. This assumption is load-bearing for the efficiency constraints and the reported overlap regions, especially the narrow interval claimed for GRS1915+105.

    Authors: We computed the ISCO location and the specific energy E_ISCO directly from the conserved quantities and effective potential of the Kerr-MOG metric, so the radiative efficiency η = 1 − E_ISCO already incorporates the modified geodesic constants. Nevertheless, we agree that the full Novikov-Thorne stress-energy tensor and flux derivation assumes the Einstein equations and would ideally be repeated from the MOG field equations. This is a standard approximation in modified-gravity accretion studies, but we will add an explicit discussion of the approximation and its limitations in the revised manuscript, with particular emphasis on the narrow interval for GRS1915+105. revision: yes

  2. Referee: [Combined constraints section] Section on combined constraints (radiative efficiency plus jet power): the overlap regions are constructed by requiring the model to reproduce the same observational efficiency and jet-power numbers used to define the input constraints. No error budgets, robustness tests against model variations, or explicit propagation of observational uncertainties are supplied, so the claimed viable regions rest on unexamined assumptions about data and model fidelity.

    Authors: The overlap regions are the intersections of the separately allowed (a, α) domains defined by each observable. We did not include a full propagation of observational errors or robustness tests, which limits the quantitative strength of the claimed regions. We will revise the manuscript to add a discussion of the main observational uncertainties and their possible effect on the size of the overlap intervals, together with a clear statement that a formal statistical error budget lies beyond the scope of the present exploratory analysis. revision: yes

Circularity Check

0 steps flagged

No significant circularity; standard observational constraints on parameters

full rationale

The paper computes ISCO locations in the Kerr-MOG metric, inserts them into the standard Novikov-Thorne binding-energy formula for radiative efficiency, and uses published observational efficiency and jet-power values to delineate allowed (a, α) regions. This is ordinary parameter-space fitting against external data, not a derivation that reduces to its own inputs by construction. No self-definitional mapping, fitted quantity relabeled as prediction, or load-bearing self-citation chain appears in the quoted abstract or described procedure. The derivation remains self-contained against the cited observational benchmarks.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central claim depends on the applicability of two standard GR models to the modified metric plus the introduction of alpha as a free parameter fitted to data.

free parameters (2)
  • modified gravity parameter α
    Extra parameter in Kerr-MOG that is varied jointly with spin to match observed efficiencies and jet powers for each source.
  • spin parameter a
    Black-hole spin that is degenerate with α and therefore fitted simultaneously to the same observables.
axioms (2)
  • domain assumption Novikov-Thorne thin-disk model determines radiative efficiency from ISCO radius
    Invoked to translate spacetime geometry into observable efficiency values.
  • domain assumption Blandford-Znajek mechanism governs jet power
    Used to predict jet energetics from black-hole parameters for the two chosen Lorentz factors.

pith-pipeline@v0.9.1-grok · 5851 in / 1428 out tokens · 25150 ms · 2026-06-25T23:06:04.678169+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

80 extracted references · 5 canonical work pages

  1. [1]

    M. S. Turner, Physics Reports333(2000), 10.1016/S0370-1573(00)00040-5. 14 0.0 0.2 0.4 0.6 0.8 1.0 0.6 0.8 1.0 1.2 1.4 α a/M Γ=2 GRS 1915+105 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.35 1.36 1.37 1.38 1.39 1.40 1.41 0.0 0.2 0.4 0.6 0.8 1.0 0.6 0.8 1.0 1.2 1.4 α a/M Γ=5 GRS 1915+105 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.35 1.36 1.37 1.38 1.39 1.40 1.41 FIG. 10. ...

    work page doi:10.1016/s0370-1573(00)00040-5 2000

  2. [2]

    B. K. Berger, Living Reviews in Relativity5, 1 (2002)

    2002

  3. [3]

    Mandelstam, Annals of Physics19(1962), 10.1016/0003-4916(62)90233-6

    S. Mandelstam, Annals of Physics19(1962), 10.1016/0003-4916(62)90233-6

    work page doi:10.1016/0003-4916(62)90233-6 1962

  4. [4]

    Nojiri and S

    S. Nojiri and S. D. Odintsov, Journal of Physics A: Math- ematical and Theoretical40, 6725 (2007)

    2007

  5. [5]

    Koyama, Reports on Progress in Physics79, 046902 (2016)

    K. Koyama, Reports on Progress in Physics79, 046902 (2016)

    2016

  6. [6]

    Shankaranarayanan and J

    S. Shankaranarayanan and J. P. Johnson, General Rela- tivity and Gravitation54, 44 (2022)

    2022

  7. [7]

    Wanget al., Journal of Cosmology and Astropar- ticle Physics2019, 046 (2019)

    H.-M. Wanget al., Journal of Cosmology and Astropar- ticle Physics2019, 046 (2019)

    2019

  8. [8]

    Narzilloev, S

    B. Narzilloev, S. Shaymatov, I. Hussain,et al., European Physical Journal C81, 849 (2021)

    2021

  9. [9]

    Atamurotov, D

    F. Atamurotov, D. Ortiqboev, A. Abdujabbarov,et al., European Physical Journal C82, 659 (2022)

    2022

  10. [10]

    Kuanget al., Physical Review D106, 064012 (2022)

    X. Kuanget al., Physical Review D106, 064012 (2022)

    2022

  11. [11]

    Maselliet al., The Astrophysical Journal843, 25 (2017)

    A. Maselliet al., The Astrophysical Journal843, 25 (2017)

    2017

  12. [12]

    Chenet al., Journal of Cosmology and Astroparticle Physics2021, 043 (2021)

    S. Chenet al., Journal of Cosmology and Astroparticle Physics2021, 043 (2021)

    2021

  13. [13]

    Bhattacharyyaet al., Physical Review D96, 064044 (2017)

    S. Bhattacharyyaet al., Physical Review D96, 064044 (2017)

    2017

  14. [14]

    Moulin, Universe5, 202 (2019)

    F. Moulin, Universe5, 202 (2019)

    2019

  15. [15]

    Akiyamaet al., The Astrophysical Journal Letters 875, L1 (2019)

    K. Akiyamaet al., The Astrophysical Journal Letters 875, L1 (2019)

    2019

  16. [16]

    B. P. Abbottet al., Physical Review Letters116, 061102 (2016)

    2016

  17. [17]

    J. W. Moffat, Journal of Cosmology and Astroparticle Physics2006, 004 (2006)

    2006

  18. [18]

    Heisenberg, Journal of Cosmology and Astroparticle Physics2018, 054 (2018)

    L. Heisenberg, Journal of Cosmology and Astroparticle Physics2018, 054 (2018)

    2018

  19. [19]

    Jamaliet al., Journal of Cosmology and Astroparticle Physics2018, 048 (2018)

    S. Jamaliet al., Journal of Cosmology and Astroparticle Physics2018, 048 (2018)

    2018

  20. [20]

    J. D. Bekenstein, Physical Review D7, 2333 (1973)

    1973

  21. [21]

    Ruppeiner, Physical Review D75, 024037 (2007)

    G. Ruppeiner, Physical Review D75, 024037 (2007)

    2007

  22. [22]

    Caiet al., Physical Review D91, 024032 (2015)

    R. Caiet al., Physical Review D91, 024032 (2015)

    2015

  23. [23]

    Iorio, Classical and Quantum Gravity31, 085003 (2014)

    L. Iorio, Classical and Quantum Gravity31, 085003 (2014)

    2014

  24. [24]

    M.Laurentiset al.,PhysicalReviewD97,104024(2018)

    2018

  25. [25]

    Panpanichet al., Physical Review D100, 044031 (2019)

    S. Panpanichet al., Physical Review D100, 044031 (2019)

    2019

  26. [26]

    Tahirasghariet al., Physical Review D106, 064021 (2022)

    F. Tahirasghariet al., Physical Review D106, 064021 (2022)

    2022

  27. [27]

    R. P. Kerr, Physical Review Letters11, 237 (1963)

    1963

  28. [28]

    Y. Cui, K. Hada, T. Kawashima, and et al., Nature621, 711 (2023)

    2023

  29. [29]

    Sharif and M

    M. Sharif and M. Shahzadi, European Physical Journal C77, 363 (2017)

    2017

  30. [30]

    Zhang and et al., Journal of Cosmology and Astropar- ticle Physics2024, 027 (2024)

    Z. Zhang and et al., Journal of Cosmology and Astropar- ticle Physics2024, 027 (2024)

    2024

  31. [31]

    Z. Xu, D. Ma, and K. Li, European Physical Journal C 86, 295 (2026)

    2026

  32. [32]

    M. A. Abramowicz and P. C. Fragile, Living Reviews in Relativity16, 1 (2013)

    2013

  33. [33]

    Sądowski, J.-P

    A. Sądowski, J.-P. Lasota, M. A. Abramowicz, and R. Narayan, Monthly Notices of the Royal Astronomi- cal Society456, 3915 (2016)

    2016

  34. [34]

    Bagchi, M

    J. Bagchi, M. Vivek, V. Vikram, A. Hota, K. G. Biju, S. K. Sirothia, R. Srianand, Gopal-Krishna, and J. Ja- cob, Astrophysical Journal788, 174 (2014)

    2014

  35. [36]

    Dickinson, Galaxies6(2018), 10.3390/galax- ies6020056

    B. Narzilloev, J. Rayimbaev, A. Abdujabbarov, and B. Ahmedov, Galaxies9(2021), 10.3390/galax- ies9030063

    work page doi:10.3390/galax- 2021

  36. [37]

    Narzilloev and B

    B. Narzilloev and B. Ahmedov, New Astron.98, 101922 (2023)

    2023

  37. [38]

    Narzilloev, A

    B. Narzilloev, A. Abdujabbarov, and A. Hakimov, In- ternational Journal of Modern Physics A37, 2250144 (2022), https://doi.org/10.1142/S0217751X22501445

    work page doi:10.1142/s0217751x22501445 2022

  38. [39]

    Narzilloev and B

    B. Narzilloev and B. Ahmedov, Symmetry15, 293 (2023)

    2023

  39. [40]

    Mirzaev, S

    T. Mirzaev, S. Li, B. Narzilloev, I. Hussain, A. Abdu- jabbarov, and B. Ahmedov, European Physical Journal Plus138, 47 (2023)

    2023

  40. [41]

    Narzilloev and B

    B. Narzilloev and B. Ahmedov, Int. J. Mod. Phys. A38, 2350026 (2023)

    2023

  41. [42]

    J. S. Spilker, J. B. Champagne, X. Fan, S. Fujimoto, P. P. van der Werf, J. Yang, and M. Yue, Astrophysical 15 Journal982, 72 (2025)

    2025

  42. [43]

    L. Gou, J. E. McClintock, J. F. Steiner, R. Narayan, A. G. Cantrell, C. D. Bailyn, and J. A. Orosz, Astro- physical Journal Letters718, L122 (2010)

    2010

  43. [44]

    J. F. Steiner, J. E. McClintock, and M. J. Reid, Astro- physical Journal Letters745, L7 (2011)

    2011

  44. [46]

    Z. Chen, L. Gou, J. E. McClintock, J. F. Steiner, J. Wu, W.Xu, J.A.Orosz, andY.Xiang,AstrophysicalJournal 825, 45 (2016)

    2016

  45. [47]

    Shafee, J

    R. Shafee, J. E. McClintock, R. Narayan, S. W. Davis, L.-X. Li, and R. A. Remillard, Astrophysical Journal 636, L113 (2005)

    2005

  46. [48]

    J. E. McClintock, R. Shafee, R. Narayan, R. A. Remil- lard, S. W. Davis, and L.-X. Li, Astrophysical Journal 652, 518 (2006)

    2006

  47. [49]

    Narzilloev and B

    B. Narzilloev and B. Ahmedov, Symmetry14(2022), 10.3390/sym14091765

    work page doi:10.3390/sym14091765 2022

  48. [51]

    Chandrasekhar,The mathematical theory of black holes, Vol

    S. Chandrasekhar,The mathematical theory of black holes, Vol. 69 (Oxford university press, 1998)

    1998

  49. [52]

    Narzilloev and B

    B. Narzilloev and B. Ahmedov, Int. J. Mod. Phys. D32, 2350064 (2023)

    2023

  50. [53]

    Saidov, B

    B. Saidov, B. Narzilloev, I. Hussain, A. Abdujabbarov, and B. Ahmedov, Phys. Rev. D112, 104057 (2025)

    2025

  51. [54]

    S. N. Zhang, W. Cui, and W. Chen, The Astrophysical Journal482, L155 (1997)

    1997

  52. [55]

    Bambi,Black holes: a laboratory for testing strong gravity, Vol

    C. Bambi,Black holes: a laboratory for testing strong gravity, Vol. 10 (Springer, 2017)

    2017

  53. [56]

    Zhang, J

    C. Zhang, J. Lewandowski, Y. Ma, and J. Yang, Physical Review D111, L081504 (2025)

    2025

  54. [57]

    J. E. McClintock, R. Narayan, and J. F. Steiner, Space Science Reviews183, 295 (2014)

    2014

  55. [58]

    M. Y. Piotrovich, E. S. Shablovinskaya, E. A. Ma- lygin, S. D. Buliga, and T. M. Natsvlishvili, Monthly Notices of the Royal Astronomical Society526, 2596 (2023), https://academic.oup.com/mnras/article- pdf/526/2/2596/51894287/stad2934.pdf

    2023

  56. [59]

    N. I. Shakura and R. A. Sunyaev, Astronomy and Astro- physics, Vol. 24, p. 337-35524, 337 (1973)

    1973

  57. [61]

    L.Kong, Z.Li, andC.Bambi,TheAstrophysicalJournal 797, 78 (2014)

    2014

  58. [62]

    S. M. M. A. N. Wilmset al., arXiv preprint astro- ph/0509028 (2005)

    arXiv 2005

  59. [63]

    I. F. Mirabel and L. F. Rodriguez, Annual Review of Astronomy and Astrophysics37, 409 (1999)

    1999

  60. [64]

    Punsly and F

    B. Punsly and F. Coroniti, Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 354, May 10, 1990, p. 583-615. 354, 583 (1990)

    1990

  61. [65]

    Koide, Physical Review D67, 104010 (2003)

    S. Koide, Physical Review D67, 104010 (2003)

    2003

  62. [66]

    R. D. Blandford and R. L. Znajek, Monthly Notices of the Royal Astronomical Society179, 433 (1977)

    1977

  63. [67]

    Tchekhovskoy, R

    A. Tchekhovskoy, R. Narayan, and J. C. McKinney, The Astrophysical Journal711, 50 (2010)

    2010

  64. [68]

    G. Pei, S. Nampalliwar, C. Bambi, and M. J. Middleton, The European Physical Journal C76, 1 (2016)

    2016

  65. [69]

    R. A. Daly, The Astrophysical Journal886, 37 (2019)

    2019

  66. [70]

    R. A. Daly, Monthly Notices of the Royal Astronomical Society500, 215 (2021)

    2021

  67. [71]

    L. Gou, J. E. McClintock, J. F. Steiner, R. Narayan, A. G. Cantrell, C. D. Bailyn, and J. A. Orosz, The As- trophysical Journal Letters718, L122 (2010)

    2010

  68. [72]

    J. F. Steiner, J. E. McClintock, and M. J. Reid, The Astrophysical Journal Letters745, L7 (2011)

    2011

  69. [73]

    J. F. Steiner, R. C. Reis, J. E. McClintock, R. Narayan, R. A. Remillard, J. A. Orosz, L. Gou, A. C. Fabian, and M. A. Torres, Monthly Notices of the Royal Astronomical Society416, 941 (2011)

    2011

  70. [74]

    Z. Chen, L. Gou, J. E. McClintock, J. F. Steiner, J. Wu, W. Xu, J. A. Orosz, and Y. Xiang, The Astrophysical Journal825, 45 (2016)

    2016

  71. [75]

    Li, and R

    R.Shafee, J.E.McClintock, R.Narayan, S.W.Davis, L.- X. Li, and R. A. Remillard, The Astrophysical Journal 636, L113 (2005)

    2005

  72. [76]

    J. E. McClintock, R. Shafee, R. Narayan, R. A. Remil- lard, S. W. Davis, and L.-X. Li, The Astrophysical Jour- nal652, 518 (2006)

    2006

  73. [77]

    Saidov, B

    B. Saidov, B. Narzilloev, A. Abdujabbarov, M. Khudoy- berdieva, and B. Ahmedov, Universe10, 454 (2024)

    2024

  74. [78]

    R. M. Wald, Phys. Rev. D10, 1680 (1974)

    1974

  75. [79]

    Penrose, Phys

    R. Penrose, Phys. Rev. Lett.14, 57 (1965)

    1965

  76. [80]

    M. J. Middleton, J. C. Miller-Jones, and R. P. Fender, Monthly Notices of the Royal Astronomical Society439, 1740 (2014)

    2014

  77. [81]

    Narzilloev and B

    B. Narzilloev and B. Ahmedov, Symmetry14, 1765 (2022)

    2022

  78. [82]

    Moscibrodzka, Astrophysics and Space Science369, 68 (2024)

    M. Moscibrodzka, Astrophysics and Space Science369, 68 (2024)

    2024

  79. [83]

    Narzilloev, A

    B. Narzilloev, A. Abdujabbarov, B. Ahmedov, and C. Bambi, Eur. Phys. J. C84, 909 (2024), arXiv:arXiv:2408.05576 [gr-qc]

    arXiv 2024

  80. [84]

    Narzilloev, A

    B. Narzilloev, A. Abdujabbarov, B. Ahmedov, and C. Bambi, Phys. Rev. D108, 103013 (2023)

    2023