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Six-dimensional Myers-Perry rotating black hole cannot be overspun

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Pith's one-line read A six-dimensional Myers-Perry black hole with two rotations cannot be overspun by linear test-particle accretion.

desk verdict A useful partial result on six-dimensional Myers-Perry overspinning, but the blanket no-overspinning claim is not established by the channel-restricted calculations shown. read the letter →

arxiv 1908.07799 v2 pith:4X4LZSJB submitted 2019-08-21 gr-qc astro-ph.HEhep-th

Sanjar Shaymatov , Naresh Dadhich , Bobomurat Ahmedov This is my paper · ORCID
classification gr-qcastro-ph.HEhep-th MSC 83C5783C75 PACS 04.50.+h04.20.Dw
keywords six-dimensionalMyers-Perryblackholeweakcosmiccensorshipoverspinningtestparticleaccretionextremalityrotatinghigherdimensionsnonlinear
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether a six-dimensional rotating (Myers-Perry) black hole with two independent rotation axes can be destroyed by throwing in a test particle. It argues that it cannot: the largest angular momentum a particle can deliver to the horizon is always smaller than the smallest amount needed to push the black hole past extremality. The authors compute the gap ΔJ = δJmax − δJmin and find it negative definite for both equal rotations (a = b) and unequal rotations (a = 2b) when the black hole starts near extremal. A negative gap means no test particle can jump over extremality and expose a naked singularity, so the weak cosmic censorship conjecture is obeyed at linear order. The paper also checks second-order perturbations, where the horizon remains intact, and conjectures the result holds in all dimensions above six.

What carries the argument

The load-bearing object is the angular-momentum gap $\Delta J = \delta J_{\rm max} - \delta J_{\rm min}$. The maximum $\delta J_{\rm max}$ is fixed by the condition that a particle falling into the horizon must satisfy $\delta E \ge \Omega_\phi\, \delta J_\phi + \Omega_\psi\, \delta J_\psi$, where $\Omega_\phi$ and $\Omega_\psi$ are the horizon angular velocities; this bounds the spin the particle can deposit. The minimum $\delta J_{\rm min}$ is set by the extremality condition—for equal rotations, $3M^2 = 4\pi^2 a^6$, with overspinning requiring $3M^2 < 4\pi^2 a^6$—and is the smallest angular momentum that would make the final state super-extremal. The paper expands both quantities near extremality using the horizon radius $r_+$ determined by $\Delta = 0$, and shows the leading-order combination is negative definite in both equal-rotation and unequal-rotation ($a=2b$) cases. For the nonlinear check, the same role is played by the perturbation function $f(\lambda)$, defined so that $f=0$ is extremality and $f<0$ would be overspinning; its first- and second-order coefficients are computed and found to keep $f(\lambda) \ge 0$.

What would settle it

Check the gap directly: evaluate $\delta J_{\rm max}$ and $\delta J_{\rm min}$ from the exact horizon equations for small but nonzero $\epsilon$ and $\delta E$, without using the paper's truncated expansions, and see whether $\Delta J = \delta J_{\rm max} - \delta J_{\rm min}$ ever turns positive for allowed particle parameters. A single positive value would break the no-overspinning claim. A more direct check is to derive the first-order-in-$\epsilon$ correction to the horizon radius from $\Delta = 0$ and verify the coefficient that enters the expression for $\delta J_{\rm max}$.

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Extended reading notes

Core claim

The paper's central claim is that the six-dimensional Myers-Perry black hole—the rotating vacuum solution of general relativity in six dimensions, here taken with two rotation parameters $a$ and $b$—cannot be overspun by linear test-particle accretion. Starting from a near-extremal black hole, the authors compare the maximum angular momentum $\delta J_{\rm max}$ a test particle can deliver through the horizon, fixed by the horizon angular velocities through $\delta E \ge \Omega_\phi\, \delta J_\phi + \Omega_\psi\, \delta J_\psi$, with the minimum angular momentum $\delta J_{\rm min}$ needed to drive the extremality condition negative. Their difference, $\Delta J = \delta J_{\rm max} - \delta J_{\rm min}$, comes out negative definite: for equal rotations $a=b$ the gap is $\Delta J = -\frac{4}{3}\bigl(\frac{3}{4\pi^2}\bigr)^{1/6}\bigl[(\frac13-\epsilon-\frac23\epsilon^2)M^{1/3}\delta E + M^{4/3}\epsilon^2 + \frac29 M^{-2/3}\delta E^2\bigr]$, and for unequal rotations $a=2b$ it is a similar negative expression. Because $\Delta J < 0$, no test particle can jump over extremality and expose a naked singularity. The same conclusion is checked at second order in the perturbation, where the function $f(\lambda)$ remains positive, so the horizon is preserved beyond linear order. The paper closes by conjecturing that this no-overspinning behavior holds for all dimensions greater than five.

Load-bearing premise

The load-bearing premise is that the near-extremal expansion of the horizon angular velocity used to derive $\delta J_{\rm max}$ is correct; the paper states these expansions without displaying the underlying series expansion of the horizon radius, and if the coefficients are wrong, the claimed negative sign of $\Delta J$ could disappear.

Editorial extensions

If this is right

  • In six dimensions, a Myers-Perry black hole with two rotations satisfies the weak cosmic censorship conjecture even when test-particle backreaction is ignored.
  • The five-dimensional two-rotation case, which can be overspun at linear order, is not generic; dimension six is protected by a negative angular-momentum gap.
  • Since $\Delta J$ is negative definite, there is no discontinuous jump across extremality of the kind proposed for four- and five-dimensional settings.
  • Including second-order perturbations keeps the perturbation function positive, so nonlinear accretion also preserves the horizon.
  • If the conjecture holds, all rotating Myers-Perry black holes in dimensions greater than five obey weak cosmic censorship under linear accretion.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The same negative-gap mechanism may hold for arbitrary nonzero ratio $a \neq b$, not just the $a=2b$ case studied here; checking a generic ratio would test whether the no-overspinning result is structural or special.
  • The pattern suggests a dimension-dependent parity: when a higher-dimensional black hole has more than one active rotation, the extremal surface is stiff enough to resist linear overspinning, whereas a single active rotation may behave differently; this could be probed in seven dimensions with three rotations.
  • A natural testable extension is charged or gauged-supergravity versions in six dimensions, where charge and rotation compete; the sign of the gap may then depend on which parameter dominates, as in five-dimensional charged rotating cases.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 4 minor

Summary. The paper studies the six-dimensional Myers-Perry black hole with two independent rotation parameters and claims that, unlike the five-dimensional two-rotation case, it cannot be overspun by linear test-particle accretion. The method is the standard threshold comparison: compute the minimum angular momentum δJmin needed to push the configuration beyond extremality, compute the maximum angular momentum δJmax that a particle can carry into the horizon from the energy condition δE ≥ Ωφ δJφ + Ωψ δJψ, and show that ΔJ = δJmax − δJmin is always negative. The authors treat the equal-rotation case a = b for three accretion scenarios and the unequal case a = 2b for one fixed partition δJφ = 2δJψ, obtaining ΔJ < 0 in each. They also perform a second-order (Sorce–Wald type) perturbation for a = b and a = 2b and find f(λ) > 0. The paper concludes that the weak cosmic censorship conjecture is always respected for six-dimensional rotating black holes under linear accretion, and conjectures the same for all dimensions greater than six.

Significance. If the central claim is correct, it is an interesting qualitative result: it would mean that six-dimensional rotating black holes behave differently from five-dimensional two-rotation black holes, where overspinning under linear accretion has been reported on the basis of threshold arguments. The paper also provides a conjecture for all higher dimensions and verifies the no-overspinning conclusion at second order for two special cases. The computations are simple and self-contained, using the known Myers–Perry metric and the exact extremality condition. However, the proof as written does not establish the universal claim stated in the title and abstract, because only selected accretion channels are analyzed. The significance is therefore conditional on closing that gap.

major comments (4)
  1. [Sec. II.A, scenario (iii)] The universal claim that no linear accretion can overspin the six-dimensional black hole requires checking all possible partitions of the infalling angular momentum between the two rotation axes. In scenario (iii), where the particle carries angular momentum about only one axis, the paper states that the minimum threshold δJmin 'again turns out to be the same' as in the previous scenarios, but no derivation is given. This is not a trivial statement: after adding δJψ only, the final configuration no longer has equal rotations, so the equal-rotation condition 3M^2 < 4π^2 a^6 used in rows (i) and (ii) is not applicable, and the full extremality function (7), which depends separately on a and b, must be analyzed. A separate calculation is needed to justify the assertion.
  2. [Sec. II.B, unequal rotations] For a ≠ b the paper treats only the ratio a = 2b and within that case only the accretion partition δJφ = 2δJψ. No argument is given that a = 2b is representative of all two-rotation black holes, and no argument is given that the fixed partition δJφ = 2δJψ is the one most favorable to overspinning. The extremality function (7) depends on a^6 − 33a^4b^2 − 33a^2b^4 + b^6 and a^2b^2(a^2−b^2)^4 separately, while the capture condition (19) is partition-dependent through Ωφ δJφ + Ωψ δJψ. The minimal threshold δJmin can in principle depend on how δE and δJ are distributed between the two channels. Without an exhaustive analysis or a proof that these special choices are extremal in the relevant sense, the title claim that the black hole 'cannot be overspun' is not supported.
  3. [Sec. II.B, Eqs. (30)–(32)] There is an inconsistency between Eq. (30) and Eq. (31). For the stated partition δJφ = 2δJψ, the total angular momentum added to the black hole is δJmax = δJφ + δJψ = 3δJψ. Solving δE ≥ (2Ωφ + Ωψ)δJψ with Ωφ = a/(r_+^2 + a^2) and Ωψ = b/(r_+^2 + b^2) yields δJmax = 3 (r_+^2+a^2)(r_+^2+b^2)/[2a(r_+^2+b^2)+b(r_+^2+a^2)] δE. Eq. (30) is exactly this expression without the factor 3, so it appears to give δJψ rather than the total. The subsequent Eq. (31), however, is three times the leading near-extremal value of Eq. (30). Thus the phrase 'From the above equation, we write' is not correct as written. While the final ΔJ in Eq. (32) is based on Eq. (31) and is consistent with the total angular momentum, the derivation needs to be corrected and the exact expression displayed, since a reader cannot reproduce the claimed expansion from Eq. (30).
  4. [Secs. II.A and II.B, near-extremal expansions] The expansions of δJmax in Eq. (21) and Eq. (31) are asserted without displaying the corresponding expansion of the horizon radius r_+ from Eqs. (8) and (23). The coefficients of the ε and ε^2 terms in these expansions are not self-evident; they require the first- and second-order shifts of r_+ away from extremality. Since the sign of ΔJ is the central result, the paper should either display these expansions or provide a derivation. The need is particularly acute for Eq. (31), where the expansion is obtained from a formula that is itself in error and includes an O(ε) horizon shift that is not accounted for. A reader cannot presently verify the algebra without repeating the entire computation.
minor comments (4)
  1. [Sec. II.B, Eq. (26)] The parameter α is introduced as 'constant ≪ 1', but from the extremality condition (25) it is actually fixed: substituting b^6 = (α/π^2)M^2 into Eq. (25) gives 2187α^2 + 7140α − 576 = 0, whose positive root is α ≃ 0.0788, not parametrically small. The text should state this relation explicitly.
  2. [Sec. II.C, Table I] The numerical values in Table I are presented without the details of the numerical evaluation of Eq. (40), so the results are not reproducible from the text alone. Providing the numerical method or the raw data would improve the paper.
  3. [General] There are several typographical errors, including 'general ly' in the abstract, 'T ashkent' in the affiliation, 'corssover' in Sec. II.C, and 'nonliner' in the sentence preceding Eq. (51). These should be corrected.
  4. [Sec. II.C, Eq. (33)] The statement that k = 0 corresponds to single rotation and k = 1 to equal rotations is slightly confusing, since k appears as a continuous ratio in the perturbation function. It would help to state explicitly that the subsequent numerical analysis uses integer values k = 1,2,3,4 for illustration.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the no-overspinning result is derived from the metric's extremality condition and the capture bound, with contextual self-citations only.

full rationale

The paper's central inequality is self-contained rather than circular. The extremality discriminator A^2 - 4B^3 (Eq. 7) is computed from the known Myers-Perry metric (Eqs. 1-3), and the overspinning threshold is obtained by solving the inequality that the final parameters violate extremality (e.g., Eqs. 11-12, 16, 26), not by assuming the conclusion. The maximum capture angular momentum follows from the horizon energy condition δE ≥ Ω_+^φ δJ_φ + Ω_+^ψ δJ_ψ (Eq. 19), which is an independent physical input for geodesic capture. ΔJ = δJ_max - δJ_min (Eqs. 22, 32) is then an algebraic difference whose sign is evaluated; negativity is the derived result, not an input. In the a=2b section, α is introduced from the extremality condition Eq. (25); although α is not numerically evaluated, the final sign in Eq. (32) is independent of α, so no fitted parameter is masquerading as a prediction. The paper's self-citations (refs. [61] and [65]) are contextual, referencing five-dimensional analogues, and are not used to derive the six-dimensional two-rotation result. Channel-restricted accretion scenarios and unshown r_+ expansions are completeness and algebra concerns, not definitional circularity.

Assumptions & free parameters 2 free parameters · 5 assumptions · 0 invented entities

The calculations rely on standard geometry, the test-particle approximation, and the Sorce-Wald variational framework. The paper adds no new entities. The a=2b restriction is a modeling choice that limits the generality of the stated conclusion.

free parameters (2)
  • epsilon = small, epsilon << 1
    Dimensionless near-extremality parameter in the initial conditions; no value fitted, but the expansions are in orders of epsilon.
  • alpha = not specified, 'constant << 1'
    Introduced in Eq. (26) to parameterize the a=2b extremality condition; its value is not fixed, but the sign of ΔJ does not depend on it.
assumptions (5)
  • domain assumption Test-particle approximation: backreaction and self-force are ignored in linear accretion.
    Explicitly stated in Sec. I: 'linear order process in which backreaction and self-force are ignored.'
  • domain assumption The horizon energy condition δE ≥ Ωφ δJφ + Ωψ δJψ is the only constraint determining whether a test particle is absorbed.
    Used to derive δJmax in Eqs. (19)-(20) and (30); standard in the gedanken-experiment program but not derived from the geodesic effective potential.
  • standard math The Myers-Perry extremality condition Eq. (7) and the near-extremal horizon properties used in the expansions are algebraically correct.
    These are calculated from the known metric; the paper presents the final expressions without the intermediate algebra.
  • domain assumption Sorce-Wald variational inequalities (δE - ΩδJ ≥ 0 and δ²E - Ωδ²J ≥ -κ/(8π)δ²A) capture the nonlinear accretion effects.
    Invoked in Sec. II C following ref. [52].
  • ad hoc to paper The cases a=b and a=2b are representative of all two-rotation six-dimensional Myers-Perry black holes.
    The conclusion is drawn for the general case, but only these two ratios are analyzed; this is an unproven extension.

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Cite this review

Pith. "Pith review of Six-dimensional Myers-Perry rotating black hole cannot be overspun." pith.science (2026). https://pith.science/paper/4X4LZSJB

@misc{pith2026190807799,
  author       = {Pith},
  title        = {Pith review of: Six-dimensional Myers-Perry rotating black hole cannot be overspun},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4X4LZSJB}},
  note         = {Machine review of arXiv:1908.07799}
}
read the original abstract

Though under nonlinear accretion, all black holes in four and higher dimensions obey the weak cosmic censorship conjecture (CCC); however, they generally violate it for linear test particle accretion with the exception of five-dimensional rotating black hole with a single rotation. In dimensions greater than five, there exists no extremal condition for black hole with single rotation and hence it can never be overspun. However, the extremal condition does exist for five-dimensional black hole with two rotations and then it could indeed be overspun under linear accretion. In this paper, we study the case of six-dimensional rotating black hole with two rotations and show that unlike the five-dimensional black hole it cannot be overspun under linear accretion. Though for nonlinear accretion, this result is anyway expected to hold good, yet we have verified it with an explicit calculation. Further, we would like to conjecture that so should be the case in all dimensions greater than six. Thus, the weak CCC may always be obeyed even at linear accretion process for rotating black hole in all dimensions greater than five.

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Works this paper leans on

68 extracted references · 23 canonical work pages · cited by 2 Pith papers

  1. [1]

    Penrose, Riv

    R. Penrose, Riv. Nuovo Cimento 1, 252 (1969)

    1969

  2. [2]

    Christodoulou, Ann

    D. Christodoulou, Ann. N. Y. Acad. Sci. 470, 147 (1986)

    work page 1986

  3. [3]

    P. S. Joshi, International Series of Monographs on Physics, Oxford: Clarendon (Oxford University Press) (1993)

    work page 1993

  4. [4]

    P. S. Joshi, The Story of Collapsing Stars: Black Holes, Naked Singulari ties, and the Cosmic Play of Quantum Gravity: (Oxford Univer sity Press) (2015)

    work page 2015

  5. [5]

    P. S. Joshi, Pramana 55, 529 (2000) , gr-qc/0006101

    work page Pith review arXiv 2000

  6. [6]

    Goswami, P

    R. Goswami, P. S. Joshi, and P. Singh, Phys. Rev. Lett. 96, 031302 (2006) , gr-qc/0506129

    arXiv 2006

  7. [7]

    In this case, we assume that a test particle’s angular momentum δJ is equally shared between the two axes, Jφ +δJ/2 and 4 Jψ +δJ/2

    to find the minimum thresh- old value of the particle angular momentum. In this case, we assume that a test particle’s angular momentum δJ is equally shared between the two axes, Jφ +δJ/2 and 4 Jψ +δJ/2. On accretion of particle, the black hole pa- rameters change as Jφ +δJ/2, Jψ +δJ/2, and M +δE. From Eq. ( 7), it then follows: 1024 243π2 (M +δE)2 < (2Jψ ...

    work page

  8. [8]

    Stuchl ´ ık and J

    Z. Stuchl ´ ık and J. Schee, Class. Quantum Grav. 29, 065002 (2012)

    work page 2012

Show all 68 references
  1. [9]

    R. S. S. Vieira, J. Schee, W. Klu´ zniak, Z. Stuchl ´ ık, and M. Abramowicz, Phys. Rev. D 90, 024035 (2014) , arXiv:1311.5820 [gr-qc]

    2014 arXiv

  2. [10]

    Harada, H

    T. Harada, H. Iguchi, and K. Nakao, Progress of Theoretical Physics 107, 449 (2002) , gr-qc/0204008

    2002 arXiv

  3. [11]

    Giacomazzo, L

    B. Giacomazzo, L. Rezzolla, and N. Ster- gioulas, Phys. Rev. D 84, 024022 (2011) , arXiv:1105.0122 [gr-qc]

    2011 arXiv

  4. [12]

    B. P. e. a. V. Abbott, Phys. Rev. Lett. 116, 061102 (2016) , arXiv:1602.03837 [gr-qc]

    2016 arXiv

  5. [13]

    Stuchl ´ ık and J

    Z. Stuchl ´ ık and J. Schee, Class. Quantum Grav. 31, 195013 (2014) , arXiv:1402.2891 [astro-ph.HE]

    2014 arXiv

  6. [14]

    Wald, Ann

    R. Wald, Ann. Phys. (N.Y.) 82, 548 (1974)

    1974

  7. [15]

    Dadhich and K

    N. Dadhich and K. Narayan, Phys. Lett. A 231, 335 (1997)

    1997

  8. [16]

    B. P. e. a. V. Abbott, Phys. Rev. Lett. 116, 241102 (2016) , arXiv:1602.03840 [gr-qc]

    2016 arXiv

  9. [17]

    Jacobson and T

    T. Jacobson and T. P. Sotiriou, Phys. Rev. Lett. 104, 021101 (2010) , arXiv:0911.3363 [gr-qc]

    2010 arXiv

  10. [18]

    Saa and R

    A. Saa and R. Santarelli, Phys. Rev. D 84, 027501 (2011) , arXiv:1105.3950 [gr-qc]

    2011 arXiv

  11. [19]

    (30) From the above equation, we write δJmax = 2 ( 1 +ǫ2) 6 √ α π2 M 1/ 3 δE

    and rewrite the maximum threshold value as δJmax = ( r2 + +a2)( r2 + +b2) 2a ( r2 + +b2) +b ( r2 + +a2) δE. (30) From the above equation, we write δJmax = 2 ( 1 +ǫ2) 6 √ α π2 M 1/ 3 δE. (31) This is the maximum threshold angular momentum. The difference between δJmax and δJmin ...

  12. [20]

    V. E. Hubeny, Phys. Rev. D 59, 064013 (1999) , gr-qc/9808043

    1999 arXiv

  13. [21]

    Shaymatov, M

    S. Shaymatov, M. Patil, B. Ahmedov, and P. S. Joshi, Phys. Rev. D 91, 064025 (2015) , arXiv:1409.3018 [gr-qc]

    2015 arXiv

  14. [22]

    G. E. A. Matsas and A. R. R. da Silva, Phys. Rev. Lett. 99, 181301 (2007) , arXiv:0706.3198 [gr-qc]

    2007 arXiv

  15. [23]

    Berti, V

    E. Berti, V. Cardoso, L. Gualtieri, F. Pretorius, and U. Sperhake, Phys. Rev. Lett. 103, 239001 (2009) , arXiv:0911.2243 [gr-qc]

    2009 arXiv

  16. [24]

    Li and C

    Z. Li and C. Bambi, Phys. Rev. D 87, 124022 (2013) , arXiv:1304.6592 [gr-qc]

    2013 arXiv

  17. [25]

    Bouhmadi-L´ opez, V

    M. Bouhmadi-L´ opez, V. Cardoso, A. Nerozzi, and J. V. Rocha, Phys. Rev. D 81, 084051 (2010) , arXiv:1003.4295 [gr-qc]

    2010 arXiv

  18. [26]

    J. V. Rocha and R. Santarelli, Phys. Rev. D 89, 064065 (2014) , arXiv:1402.4840 [gr-qc]

    2014 arXiv

  19. [27]

    D¨ uzta¸ s and M

    K. D¨ uzta¸ s and M. Jamil, Mod. Phys. Lett. A 34, 1950248 (2019) , arXiv:1812.06966 [gr-qc]

    2019 arXiv

  20. [28]

    S. Jana, R. Shaikh, and S. Sarkar, Phys. Rev. D 98, 124039 (2018) , arXiv:1808.09656 [gr-qc]

    2018 arXiv

  21. [29]

    D¨ uzta¸ s, Class

    K. D¨ uzta¸ s, Class. Quantum Grav. 35, 045008 (2018) , arXiv:1710.06610 [gr-qc]

    2018 arXiv

  22. [30]

    Barausse, V

    E. Barausse, V. Cardoso, and G. Khanna, Phys. Rev. Lett. 105, 261102 (2010) , arXiv:1008.5159 [gr-qc]

    2010 arXiv

  23. [31]

    D¨ uzta¸ s, M

    K. D¨ uzta¸ s, M. Jamil, S. Shaymatov, and B. Ahmedov, arXiv e-prints (2018), arXiv:1808.04711 [gr-qc]

    2018 arXiv

  24. [32]

    Y. Song, M. Zhang, D.-C. Zou, C.-Y. Sun, and R.-H. Yue, Commun. Theor. Phys. 69, 694 (2018) , arXiv:1705.01676 [gr-qc]

    2018 arXiv

  25. [33]

    Isoyama, N

    S. Isoyama, N. Sago, and T. Tanaka, Phys. Rev. D 84, 124024 (2011) , arXiv:1108.6207 [gr-qc]

    2011 arXiv

  26. [34]

    Zimmerman, I

    P. Zimmerman, I. Vega, E. Poisson, and R. Haas, Phys. Rev. D 87, 041501 (2013) , arXiv:1211.3889 [gr-qc]

    2013 arXiv

  27. [35]

    (38) For an optimal choice of linear particle accretion, we take the minimum possible value of δE absorbed by black hole as per the Sorce and Wald [ 52] new gedanken exper- iment

    and ( 36), let us substitute f1 and f2 in the above equation for first and second order perturba- tions, and write 6 f (λ) = 576 M 4ǫ2 + 9437184M 16 + 2239488 ( 33k2 + 33k4 −k6 − 1 ) π2M 8J 6 + 43046721k2( k2 − 1 ) 4 π4J 12 4096M 13 ( δE − ΩδJ ) λ + 1 2 [ 9437184M 16 + 2239488 ...

    2019

  28. [36]

    J. V. Rocha and V. Car- doso, Phys. Rev. D 83, 104037 (2011) , arXiv:1102.4352 [gr-qc]

    2011 arXiv

  29. [37]

    Colleoni and L

    M. Colleoni and L. Barack, Phys. Rev. D 91, 104024 (2015) , arXiv:1501.07330 [gr-qc]

    2015 arXiv

  30. [38]

    Colleoni, L

    M. Colleoni, L. Barack, A. G. Shah, and M. van de Meent, Phys. Rev. D 92, 084044 (2015) , arXiv:1508.04031 [gr-qc]

    2015 arXiv

  31. [39]

    Shaymatov, Int

    S. Shaymatov, Int. J. Mod. Phys.: Conf. Ser. 49, 1960020 (2019)

    2019

  32. [40]

    Semiz, Gen

    I. Semiz, Gen. Relativ. Gravit. 43, 833 (2011) , gr-qc/0508011

    2011 arXiv

  33. [41]

    G. Z. T´ oth, Gen. Relativ. Gravit. 44, 2019 (2012) , arXiv:1112.2382 [gr-qc]

    2012 arXiv

  34. [42]

    D¨ uzta¸ s and ˙I

    K. D¨ uzta¸ s and ˙I. Semiz, Phys. Rev. D 88, 064043 (2013) , arXiv:1307.1481 [gr-qc]

    2013 arXiv

  35. [43]

    D¨ uzta¸ s, Gen

    K. D¨ uzta¸ s, Gen. Relativ. Gravit. 46, 1709 (2014) , arXiv:1312.7361 [gr-qc]

    2014 arXiv

  36. [44]

    Semiz and K

    I. Semiz and K. D¨ uzta¸ s, Phys. Rev. D 92, 104021 (2015) , arXiv:1507.03744 [gr-qc]

    2015 arXiv

  37. [45]

    Gwak, arXiv e-prints , arXiv:1910.13329 (2019), arXiv:1910.13329 [gr-qc]

    B. Gwak, arXiv e-prints , arXiv:1910.13329 (2019), arXiv:1910.13329 [gr-qc]

    2019 arXiv

  38. [46]

    Gwak and B.-H

    B. Gwak and B.-H. Lee, J. Cosmol. Astropart. Phys. 02, 015 (2016) , arXiv:1509.06691 [gr-qc]

    2016 arXiv

  39. [47]

    Nat´ ario, L

    J. Nat´ ario, L. Queimada, and R. Vi- cente, Class. Quantum Grav. 33, 175002 (2016) , 10 arXiv:1601.06809 [gr-qc]

    2016 arXiv

  40. [48]

    Nat´ ario and R

    J. Nat´ ario and R. Vicente, Gen. Relativ. Gravit. 52, 5 (2020) , arXiv:1908.09854 [gr-qc]

    2020 arXiv

  41. [49]

    Israel, Phys

    W. Israel, Phys. Rev. Lett. 57, 397 (1986)

    1986

  42. [50]

    A. K. Mishra and S. Sarkar, Phys. Rev. D 100, 024030 (2019) , arXiv:1905.00394 [gr-qc]

    2019 arXiv

  43. [51]

    B. C. J.M. Bardeen and S. Hawking, Commun. Math. Phys. 31, 161 (1973)

    1973

  44. [52]

    H. M. Siahaan, Phys. Rev. D 93, 064028 (2016) , arXiv:1512.01654 [gr-qc]

    2016 arXiv

  45. [53]

    D¨ uzta¸ s, Phys

    K. D¨ uzta¸ s, Phys. Rev. D 94, 124031 (2016) , arXiv:1701.07241 [gr-qc]

    2016 arXiv

  46. [54]

    Chakraborty, P

    C. Chakraborty, P. Kocherlakota, and P. S. Joshi, Phys. Rev. D 95, 044006 (2017) , arXiv:1605.00600 [gr-qc]

    2017 arXiv

  47. [55]

    Sorce and R

    J. Sorce and R. M. Wald, Phys. Rev. D 96, 104014 (2017) , arXiv:1707.05862 [gr-qc]

    2017 arXiv

  48. [56]

    R. M. Wald, Int. J. Mod. Phys. D 27, 1843003 (2018)

    2018

  49. [57]

    J. An, J. Shan, H. Zhang, and S. Zhao, Phys. Rev. D 97, 104007 (2018) , arXiv:1711.04310 [hep-th]

    2018 arXiv

  50. [58]

    B. Gwak, J. High Energy Phys. 09, 81 (2018) , arXiv:1807.10630 [gr-qc]

    2018 arXiv

  51. [59]

    B. Ge, Y. Mo, S. Zhao, and J. Zheng, Phys. Lett. B 783, 440 (2018) , arXiv:1712.07342 [hep-th]

    2018 arXiv

  52. [60]

    B. Ning, B. Chen, and F.-L. Lin, Phys. Rev. D 100, 044043 (2019) , arXiv:1902.00949 [gr-qc]

    2019 arXiv

  53. [61]

    Wang and J

    X.-Y. Wang and J. Jiang, arXiv e-prints , arXiv:1911.03938 (2019), arXiv:1911.03938 [hep-th]

    2019 arXiv

  54. [62]

    He and J

    Y.-L. He and J. Jiang, Phys. Rev. D 100, 124060 (2019) , arXiv:1912.05217 [hep-th]

    2019 arXiv

  55. [63]

    Jiang, (2019), arXiv:1912.10826 [gr-qc]

    J. Jiang, (2019), arXiv:1912.10826 [gr-qc]

    2019 arXiv

  56. [64]

    Shaymatov, N

    S. Shaymatov, N. Dadhich, and B. Ahmedov, Eur. Phys. J. C 79, 585 (2019) , arXiv:1809.10457 [gr-qc]

    2019 arXiv

  57. [65]

    S. W. Hawking, C. J. Hunter, and M. M. Taylor-Robinson, Phys. Rev. D 59, 064005 (1999) , hep-th/9811056

    1999 arXiv

  58. [66]

    R. C. Myers and M. J. Perry, Ann. Phys. (N.Y.) 172, 304 (1986)

    1986

  59. [67]

    Chong, M

    Z.-W. Chong, M. Cvetiˇ c, H. L¨ u, and C. N. Pope, Phys. Rev. Lett. 95, 161301 (2005) , hep-th/0506029

    2005 arXiv

  60. [68]

    Shaymatov, N

    S. Shaymatov, N. Dadhich, B. Ahmedov, and M. Jamil, arXiv e-prints (2019), arXiv:1908.01195 [gr-qc]

    2019 arXiv

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Reviewed August 14, 2026 · model on record in the stance chip above.