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REVIEW 4 major objections 4 minor 65 references

Thermodynamics of charged and accelerating black holes

T0 review · 4 major / 4 minor · reviewed 2026-08-10 · deepseek-v4-flash

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Pith's one-line read Two standard free-energy prescriptions disagree for accelerating black holes with cosmic strings, and the paper derives the exact gap plus a modified entropy that would reconcile them.

desk verdict Honest and useful reassessment of accelerating black hole thermodynamics, but the headline free-energy discrepancy is a convention-dependent statement, not a derived physical effect. read the letter →

arxiv 2501.13679 v2 pith:EJ5DETUA submitted 2025-01-23 gr-qc hep-th

Tomáš Hale , David Kubizňák , Jana Menšíková , Robert B. Mann , Jiayue Yang This is my paper · ORCID
classification gr-qchep-th MSC 83C5783C2083C40 PACS 04.70.Dy04.20.Jb
keywords acceleratingblackholesC-metricholethermodynamicscosmicstringsholographicrenormalizationtopologicalModMaxelectrodynamicsReg
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

Charged, slowly accelerating anti-de Sitter black holes hang on cosmic strings whose tensions make their thermodynamics delicate: the standard setup needs an extra normalization of the time-like Killing vector before a first law holds. The paper shows this normalization can be removed by reparametrizing the C-metric, and then computes the Euclidean free energy by two different renormalization schemes. The central result is that the standard holographic counterterm method and the topological-renormalization method agree only when the total cosmic-string tension vanishes, and otherwise differ by $2\pi\ell^2\mu_+ T$, giving $F_T = F + 2\pi\ell^2\mu_+ T$. The same gap appears for accelerating black holes in Maxwell, ModMax, and RegMax electrodynamics, and it points toward an entropy $S - 2\pi\ell^2\mu_+$ instead of the bare area law for a string-framed black hole. A curious reader should care because this reveals an unresolved ambiguity in black-hole thermodynamics that comes from cosmic-string boundary terms rather than from the electrodynamic field content.

What carries the argument

The load-bearing object is the Euclidean action evaluated by two competing renormalization schemes. Standard holographic renormalization adds boundary counterterms to the bulk action; topological renormalization instead removes divergences with a bulk Gauss-Bonnet term plus a boundary Chern form, normalized by the constant $S_0 = -\pi\ell^2$ fixed on Schwarzschild-AdS. For a C-metric with conical defects the two prescriptions differ by $2\mu_+ S_0$, so the free energies differ by $2\pi\ell^2\mu_+ T$. A second piece of machinery is the boost-Killing normalization $\omega$, fixed by requiring the free energy to reproduce the area-law entropy; the parametrization freedom of the integration constants lets the paper set $\omega = 1$ and thereby simplify the thermodynamics.

What would settle it

Compute the Euclidean action for a charged accelerating AdS C-metric with nonzero total string tension using a scheme-independent method, such as a covariant phase-space or regulated Hamiltonian calculation, and compare with the two renormalized results. Agreement with the standard counterterm result and the area-law entropy would make the topological discrepancy a scheme artifact; agreement with $F_T$ and $S - 2\pi\ell^2\mu_+$ would make the modified thermodynamics the physical one.

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Extended reading notes

Core claim

The paper works in a general parametrization of the charged C-metric and constructs extended first laws and mass formulas whose conjugate pairs include mass, entropy, electric charge, cosmic-string tensions, and pressure. It finds that the boost-Killing normalization $\omega$ can be eliminated, for instance set to one, by a suitable choice of the integration constant $c_2$, and that this choice changes which thermodynamic ensemble is natural. The main discovery is the free-energy identity $F_T = F + 2\pi\ell^2\mu_+ T = M - \phi Q - T(S - 2\pi\ell^2\mu_+)$, where $F$ is the standard holographically renormalized free energy, $F_T$ the topologically renormalized one, and $\mu_+$ the symmetrized cosmic-string tension. The identity holds in Maxwell theory and extends to ModMax and RegMax nonlinear electrodynamics. In the RegMax case, and in a specially parametrized Maxwell case, the electrostatic potential must be computed by the generalized boundary prescription rather than evaluated directly on the horizon, and that potential acquires a correction whose origin the paper leaves unexplained. The paper concludes that the thermodynamics of charged accelerating black holes is not yet fully settled.

Load-bearing premise

The derivation fixes the boost normalization $\omega$ by requiring the free energy to yield the area-law entropy $S = \text{Area}/4$; if the correct entropy for a black hole with conical defects is instead $S - 2\pi\ell^2\mu_+$, then $\omega$, the first law, and the mass formula all shift.

Editorial extensions

If this is right

  • If the identity is correct, the two renormalization schemes agree exactly when the total cosmic-string tension vanishes, so the discrepancy is observable only for string-framed black holes with a net conical deficit.
  • Adopting the modified entropy $S - 2\pi\ell^2\mu_+$ would keep the standard mass, charge, and potentials intact under topological renormalization, but would force the boost normalization and the first law to be re-derived.
  • The parametrization freedom of the C-metric is physical rather than a gauge choice, since choosing $c_2$ can eliminate the boost normalization or set the total tension to zero and changes the thermodynamic ensemble and phase behavior.
  • For RegMax accelerating black holes, the boundary prescription for the electrostatic potential produces a correction consistent with the topological action, and completing the first law requires an as-yet-unknown boost normalization $\omega$.

Reading between the lines

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

  • Beyond the paper, the disagreement suggests that cosmic strings contribute their own boundary terms to the gravitational action, so the area law may be only an approximation for C-metric black holes and a string-corrected entropy would enter the first law.
  • Beyond the paper, the RegMax potential correction, written formally as the difference of potentials at two radii, resembles the way the angular velocity of a rotating black hole is measured relative to infinity; pursuing that analogy could supply the missing boost normalization and close the first law.
  • Beyond the paper, repeating the comparison for rotating accelerating black holes or in three spacetime dimensions would test the claimed universality of the $2\pi\ell^2\mu_+ T$ gap.
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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 revisits the thermodynamics of charged, slowly accelerating AdS C-metric black holes in Maxwell, ModMax, and RegMax nonlinear electrodynamics. The authors introduce a general parametrization with two integration constants c1 and c2, derive thermodynamic quantities and extended first laws, and show that the boost Killing-vector normalization ω can be fixed by requiring consistency with the Bekenstein-Hawking entropy. They then compute the Euclidean action using both holographic renormalization and topological renormalization, claiming that in the presence of a nonzero total cosmic string tension μ+ the two free energies differ by FT = F + 2πℓ²μ+T, equivalently a modified entropy S̃ = S − 2πℓ²μ+. The claim is extended to ModMax and RegMax electrodynamics, with a modified electrostatic potential emerging for RegMax from the Hawking-Ross prescription. The paper explicitly leaves the RegMax first law unverified and ω unspecified, and it presents an alternative interpretation in which the discrepancy is absorbed into a modified Euler characteristic.

Significance. The central claim, Eq. (93), would be significant if established: it would show that topological renormalization and holographic renormalization assign different free energies and entropies to accelerating black holes with conical deficits, potentially modifying the entropy law for such spacetimes. The paper also offers a useful general parametrization that recovers and extends previous results, and it identifies a nontrivial electrostatic-potential modification in RegMax theory. The presentation is honest about the limitations of the RegMax analysis. However, the significance is conditional on resolving the status of Eq. (57), which is asserted rather than derived, and on completing the RegMax first law. The paper does not provide machine-checked proofs or reproducible code, but the Maxwell and ModMax first-law statements are explicitly verified algebraically.

major comments (4)
  1. [II.E.2, Eq. (57)] The relation SE = ST + 2μ+S0, which is the sole source of the claimed free-energy discrepancy, is asserted without showing the explicit evaluation of the bulk Gauss-Bonnet integral ∫G and the boundary Chern form for the Euclidean C-metric. The smooth-manifold value χ(M)=2 used to fix S0 in Eq. (56) is not justified for a spacetime with conical singularities on the cosmic strings. The paper's own alternative in Eqs. (59)-(60), replacing χ(M) with the orbifold value 2−4μ+, changes S0 to S0(1−2μ+) and makes the two actions agree identically. As written, Eq. (93) is therefore a convention-dependent statement about how to treat topological renormalization on singular spacetimes, not a derived consequence.
  2. [II.D, Eqs. (50)-(51)] The derivation of the boost normalization ω fixes ω by imposing the Bekenstein-Hawking area law S=Area/4 and then solving partial differential equations for ω. This is a self-consistency condition, not an independent prediction: if the entropy were instead the modified value S̃=S−2πℓ²μ+ suggested in Sec. II.E.2, then ω and the first law would change. The paper leaves this ambiguity unresolved, which weakens the abstract's claim that the parametrization 'eliminates' the nontrivial normalization of the boost Killing vector.
  3. [IV.B, Eqs. (90)-(92)] For RegMax electrodynamics, ω is explicitly left unspecified and the extended first law (90) is not verified. Nevertheless, Eq. (92) states that the topological renormalization result FT + 2μ+S0T = F holds, and Sec. V repeats that Eq. (93) is valid 'in all three cases.' Since the RegMax case lacks both the derivation of Eq. (57) and the verification of the first law, the claimed universality of Eq. (93) is not established for RegMax.
  4. [III.B, Eq. (70)] The ModMax result FT = F − 2μ+S0T is stated as 'verified' but the computation is not shown. Because this result inherits the unshown Eq. (57) from the Maxwell case, the ModMax extension does not independently support the central claim; the authors should either provide the calculation or clearly state that it is an analogous assertion.
minor comments (4)
  1. [II.B, Eq. (28)] The notation μ+ is reused for both the individual north-pole tension and the symmetric combination μ+ + μ−; although this is eventually defined in the text, it is confusing and should be disambiguated with a different symbol, e.g. μΣ.
  2. [Appendix A, Fig. 1] The special parametrization c2=2A²e² introduces a new root x=0 in hM, and the thermodynamic integrals are restricted to x∈(0,1). The text should state explicitly which compactification and Euler characteristic are used for this restricted range, since this affects the interpretation of the topological renormalization comparison.
  3. [II.D, Eq. (51)] The sentence 'A dimensional argument then implies that the proportionality factor in (51) is just a constant' is terse; spelling out the dimensional analysis would help the reader verify that no additional scale-dependent factor is allowed.
  4. [V, Conclusions] The conclusions present Eq. (93) as a finding while also acknowledging that the RegMax first law is unverified and that the origin of the modified potential is unexplained; the wording should more prominently separate the established Maxwell/ModMax results from the conjectural RegMax extension.

Circularity Check

2 steps flagged · score 3.0 of 10

The central free-energy discrepancy is largely a convention about the Euler characteristic assigned to the conical C-metric, and the boost normalization is solved for by imposing the assumed area entropy; the main scheme comparisons are otherwise independent.

  1. fitted input called prediction [Sec. II.D, Eqs. (23), (50), (51)]
    "since S is given by the Bekenstein area law, (23), the first relation can be used to derive the unknown factor ω. ... employing the entropy formula (50), imposing 0 = δϕ = δµ+ = δµ− = δP. ... treating these as independent and comparing the result with (23) then yields two partial differential equations for ω = ω(e, A, ℓ, c2), whose integration yields precisely ω ∝ sqrt[(4A^2e^2 - c2)(2 - 4A^4e^2ℓ^2 + A^2c2ℓ^2)] (51)."

    The normalization ω is not obtained from an independent first-principles condition; it is fixed by demanding that the free-energy derivative -∂F/∂T computed from the Euclidean action reproduce the Bekenstein-Hawking area entropy S = Area/4. Since T itself depends on ω, the subsequent first law and free-energy relations in the general parametrization are self-consistency consequences of this fitted normalization rather than independent predictions. This is a legitimate way to fix a coordinate/Killing normalization, but it is a fit to the assumed entropy, not a derivation of entropy or of thermodynamics.

  2. self definitional [Sec. II.E.2, Eqs. (57)-(59) and footnote 6]
    "Using naively the prescription (55) with S0 given by (56) yields SE = ST + 2µ+S0, (57) ... Alternatively, in accordance with standard thermodynamics, let us believe that topological renormalization should yield SE even in the case of accelerated black holes and for any µ+. This can be achieved by replacing S0 in (56) by S0(1 − 2µ+). Formally, this amounts to replacing in (53) χ(M) = 2 → χ(M) + const. = 2 − 4µ+, (59)."

    The claimed central result, Eq. (93), FT = F + 2πℓ²µ+T, rests on Eq. (57), which is asserted by 'naively' keeping S0 fixed by the smooth Schwarzschild-AdS case with χ(M)=2. The paper does not show the explicit evaluation of the bulk Gauss-Bonnet or boundary Chern integrals for the conically singular C-metric. Its own alternative, replacing χ(M)=2 by the orbifold Euler characteristic χ=2−4µ+ (footnote 6, from [43]), makes the two actions agree identically. Thus the discrepancy is not a forced derived consequence; it is equivalent to a convention about how topological renormalization is extended to singular spacetimes, and it disappears under the equally available prescription.

full rationale

The paper contains substantial independent content: a new parametrization of the charged C-metric, the explicit ω=1 and zero-overall-tension families, the Maxwell holographic-renormalization action, and new RegMax thermodynamic quantities. The self-citations to [18], [33], and [39] are used for exact solutions and prior thermodynamics; they are not invoked as uniqueness theorems to forbid alternatives, so they are not load-bearing circularity. The RegMax electrostatic potential is obtained from an independent Hawking-Ross boundary prescription, and its agreement with the topological action is presented as a consistency check, not as a fit. The genuinely convention-dependent point is Eq. (57)/(93): the paper openly displays the alternative S0→S0(1−2µ+) and the orbifold Euler characteristic 2−4µ+, which would erase the discrepancy; without an explicit computation of the Gauss-Bonnet/Chern integrals for the C-metric, the claimed difference is a chosen renormalization convention rather than a demonstrated prediction. Separately, the derivation of ω by imposing the area-law entropy is a self-consistency fit. These issues make the central claim partially definitional, but they are acknowledged in the text and do not amount to a hidden circular derivation or a forced self-citation chain; hence a moderate score is appropriate.

Assumptions & free parameters 2 free parameters · 6 assumptions · 1 invented entities

The central claims rest on standard AdS/CFT renormalization tools, the slow-acceleration C-metric framework, and the assumption that the area law entropy persists. The main manual input is the boost normalization ω, fixed by a consistency condition, and the parametrization freedom c2. No new particles or forces are introduced; the only invented quantity is a speculative modified entropy.

free parameters (2)
  • ω (boost Killing vector normalization) = sqrt((4A²e² - c2)(2 - 4A⁴e²ℓ² + A²c2ℓ²))/2 for Maxwell/ModMax; left unspecified for RegMax
    Chosen by imposing that the free energy derived from the Euclidean action reproduces the Bekenstein-Hawking entropy (Sec. II.D); it is not derived from an independent physical principle.
  • c2 (integration constant / parametrization freedom) = Arbitrary; special choices: 2A²e², 4A²e² - 2K, or expression (41) for ω=1
    A free integration constant of the C-metric solution, exploited to simplify thermodynamics; its choice is physical (affects string tensions and ensemble), so it is a manually chosen parameter.
assumptions (6)
  • domain assumption The semiclassical approximation equating the free energy to the on-shell Euclidean action over its period, F = S_E/β, is valid for these spacetimes.
    Used throughout; standard but non-trivial for spacetimes with conical singularities.
  • domain assumption The standard AdS counterterm action (47) renders the Euclidean action finite and defines the correct thermodynamics.
    Sec. II.D; this is the benchmark against which topological renormalization is compared.
  • domain assumption The topological renormalization prescription (55), with S0 = -πℓ² fixed by the Schwarzschild-AdS solution, applies to C-metric spacetimes.
    Sec. II.E; this is the assumption whose breakdown produces the discrepancy; the paper itself questions it.
  • domain assumption The extended first law of black hole thermodynamics, with conjugate pairs (T,S), (φ,Q), (λ±,μ±), (V,P), holds.
    The framework is imposed and used to fix ω and verify consistency; not proven from a variational principle here.
  • domain assumption The Bekenstein-Hawking area law S = Area/4 is the correct entropy for accelerating black holes.
    Used to fix ω (Sec. II.D); the paper later suggests S̃ = S - 2πℓ²μ₊ as an alternative, so this assumption is load-bearing and potentially false.
  • domain assumption For RegMax, the generalized Hawking-Ross prescription (85) gives the correct electrostatic potential.
    Sec. IV.B; yields φ that differs from the naive horizon potential, and its origin is unexplained.
invented entities (1)
  • Modified entropy S̃ = S - 2πℓ²μ₊
    purpose: To reconcile the topological renormalization free energy with standard thermodynamics (Eqs. 58, 93).
    It is proposed as one possible interpretation; no independent derivation or observational handle is given, and the paper leaves its status open.

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Pith. "Pith review of Thermodynamics of charged and accelerating black holes." pith.science (2026). https://pith.science/paper/EJ5DETUA

@misc{pith2026250113679,
  author       = {Pith},
  title        = {Pith review of: Thermodynamics of charged and accelerating black holes},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EJ5DETUA}},
  note         = {Machine review of arXiv:2501.13679}
}
read the original abstract

We reconsider various C-metric spacetimes describing charged and (slowly) accelerating AdS black holes in different theories of (non-linear) electrodynamics and revisit their thermodynamic properties. Focusing first on the Maxwell theory, we find a parametrization of the metric where we can eliminate the non-trivial `normalization' of the boost Killing vector which was crucial for obtaining consistent thermodynamics in previous studies. We also calculate the Euclidean action using i) the standard holographic renormalization and ii) using the topological renormalization, showing that in the presence of overall cosmic string tension the two do not agree. These results are also extended to accelerating black holes in ModMax and RegMax non-linear electrodynamics. Interestingly, for the latter the electrostatic potential picks up a modification, that remains to be explained, but is consistent with the topological renormalization and the (generalized) Hawking--Ross prescription. Our study indicates that thermodynamics of charged accelerating black holes is far from being completely understood.

Figures

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Figure 1
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Works this paper leans on

65 extracted references · 23 canonical work pages

  1. [1]

    snapping swallow tails,

    Standard parametrization First, as a sanity check, let us make the following standard choice (see e.g. [16, 18]): c1 = −12m , c2 = 2A2e2 − 2 . (38) It is easy to verify that upon such a choice, we recover the metric functions and thermodynamic charges presented in [18], namely fM = 1 − A2r2 1 − 2m r + e2 r2 + r2 ℓ2 , h M = 1 − x2 1 + 2Amx + A2e2x2 , M = m...

    work page

  2. [2]

    (40) 7 The former is possible, as the asymptotics of the charged C-metric is affected by the acceleration, cf

    Normalized Killing vector Perhaps more interesting is to choose the parametersc1 and c2 to eliminate ω and to simplify the physical mass, namely to set ω = 1 , M = m K . (40) 7 The former is possible, as the asymptotics of the charged C-metric is affected by the acceleration, cf. (18). Thus, by reparametrizing c2, one may affect the effective normalizatio...

    work page

  3. [3]

    NUTty spacetimes

    Vanishing overall tension Of course many other useful parametrizations are possible. To present a final example, we set c1 = −12m , c2 = 4A2e2 − 2K , (43) yielding µ+ = 0 , µ − = Am K . (44) While this would seem to be a mere parameter choice forc2, this is not the case. It corresponds to a physical choice of the distribution of the strings, as is obvious...

    work page

  4. [4]

    J. F. Plebanski and M. Demianski, Rotating, charged, and uniformly accelerating mass in general relativity, Annals Phys. 98, 98 (1976)

    work page 1976

  5. [5]

    (52) On a four-dimensional manifold without boundaries, the Euler theorem states that R M d4xG = 32 π2χ(M ), where χ(M ) is the Euler characteristic [51]

    Basic idea The idea is to consider a bulk integral of a topological Gauss-Bonnet term: G = Rµναβ Rµναβ − 4RµνRµν + R2 . (52) On a four-dimensional manifold without boundaries, the Euler theorem states that R M d4xG = 32 π2χ(M ), where χ(M ) is the Euler characteristic [51]. On a manifold with boundary we get a correction [52] Z M d4x√g G = 32π2χ(M ) + Z ∂...

    work page

  6. [6]

    looks like

    Topological renormalization for accelerating black holes Let us now apply topological renormalization to charged accelerating black holes. Using naively the prescription (55) with S0 given by (56) yields SE = ST + 2µ+S0 , (57) where µ+ is given by (28). Clearly unlessµ+ = 0 the two actions no longer agree.5 If we take the above actionST seriously, we have...

    work page

  7. [7]

    Weyl, The theory of gravitation, Annalen Phys.54, 117 (1917)

    H. Weyl, The theory of gravitation, Annalen Phys.54, 117 (1917)

    1917

  8. [8]

    Ehlers and W

    J. Ehlers and W. Kundt,Exact solutions of the gravitational field equations(John Wiley & Sons, 1962) pp. 49–101

    work page 1962

Show all 65 references
  1. [9]

    Kinnersley and M

    W. Kinnersley and M. Walker, Uniformly accelerating charged mass in general relativity, Phys. Rev. D2, 1359 (1970)

    1970

  2. [10]

    Astorino and A

    M. Astorino and A. Viganò, Charged and rotating multi-black holes in an external gravitational field, Eur. Phys. J. C82, 829 (2022), arXiv:2105.02894 [gr-qc]

    2022 arXiv

  3. [11]

    Podolsky, Accelerating black holes in anti-de Sitter universe, Czech

    J. Podolsky, Accelerating black holes in anti-de Sitter universe, Czech. J. Phys.52, 1 (2002), arXiv:gr-qc/0202033

    2002 arXiv

  4. [12]

    Podolsky, M

    J. Podolsky, M. Ortaggio, and P. Krtous, Radiation from accelerated black holes in an anti-de Sitter universe, Phys. Rev. D 68, 124004 (2003), arXiv:gr-qc/0307108

    2003 arXiv

  5. [13]

    J. B. Griffiths and J. Podolsky, A New look at the Plebanski-Demianski family of solutions, Int. J. Mod. Phys. D15, 335 (2006), arXiv:gr-qc/0511091

    2006 arXiv

  6. [14]

    F. J. Ernst, Removal of the nodal singularity of the c-metric, Journal of Mathematical Physics17, 515 (1976)

    1976

  7. [15]

    Astorino, Thermodynamics of Regular Accelerating Black Holes, Phys

    M. Astorino, Thermodynamics of Regular Accelerating Black Holes, Phys. Rev. D95, 064007 (2017), arXiv:1612.04387 [gr-qc]

    2017 arXiv

  8. [16]

    Appels, R

    M. Appels, R. Gregory, and D. Kubiznak, Thermodynamics of Accelerating Black Holes, Phys. Rev. Lett.117, 131303 (2016), arXiv:1604.08812 [hep-th]

    2016 arXiv

  9. [17]

    Astorino, Accelerating and charged type I black holes, Phys

    M. Astorino, Accelerating and charged type I black holes, Phys. Rev. D108, 124025 (2023), arXiv:2307.10534 [gr-qc]

    2023 arXiv

  10. [18]

    AdS-like

    (see, however, a discussion in [22]). In this paper, we revisit the formulation of the thermodynamics of four-dimensional charged slowly accelerated AdS black holes. We explore the full parametric freedom of the C-metric solution and find that consistent thermodynamics can be ...

    2025 arXiv

  11. [19]

    Barrientos, A

    J. Barrientos, A. Cisterna, and K. Pallikaris, Plebanśki–Demiański à la Ehlers–Harrison: exact rotating and accelerating type I black holes, Gen. Rel. Grav.56, 111 (2024), arXiv:2309.13656 [gr-qc]

    2024 arXiv

  12. [20]

    Lü and J

    H. Lü and J. F. Vázquez-Poritz, C-metrics in gauged stu supergravity and beyond, Journal of High Energy Physics2014, 1 (2014)

    2014

  13. [21]

    Ball and N

    A. Ball and N. Miller, Accelerating black hole thermodynamics with boost time, Class. Quant. Grav.38, 145031 (2021), arXiv:2008.03682 [hep-th]

    2021 arXiv

  14. [22]

    Ball, Global first laws of accelerating black holes, Class

    A. Ball, Global first laws of accelerating black holes, Class. Quant. Grav.38, 195024 (2021), arXiv:2103.07521 [hep-th]

    2021 arXiv

  15. [23]

    Anabalón, M

    A. Anabalón, M. Appels, R. Gregory, D. Kubizňák, R. B. Mann, and A. Ovgün, Holographic Thermodynamics of Accelerating Black Holes, Phys. Rev. D98, 104038 (2018), arXiv:1805.02687 [hep-th]

    2018 arXiv

  16. [24]

    Anabalón, F

    A. Anabalón, F. Gray, R. Gregory, D. Kubizňák, and R. B. Mann, Thermodynamics of Charged, Rotating, and Accelerating Black Holes, JHEP04, 096, arXiv:1811.04936 [hep-th]

    arXiv

  17. [25]

    Gregory and A

    R. Gregory and A. Scoins, Accelerating Black Hole Chemistry, Phys. Lett. B796, 191 (2019), arXiv:1904.09660 [hep-th]

    2019 arXiv

  18. [26]

    Appels, R

    M. Appels, R. Gregory, and D. Kubiznak, Black Hole Thermodynamics with Conical Defects, JHEP 05, 116, arXiv:1702.00490 [hep-th]

    arXiv

  19. [27]

    Emparan, C

    R. Emparan, C. V. Johnson, and R. C. Myers, Surface terms as counterterms in the AdS / CFT correspondence, Phys. Rev. D60, 104001 (1999), arXiv:hep-th/9903238

    1999 arXiv

  20. [28]

    H. Kim, N. Kim, Y. Lee, and A. Poole, Thermodynamics of accelerating AdS4 black holes from the covariant phase space, Eur. Phys. J. C83, 1095 (2023), arXiv:2306.16187 [hep-th]

    2023 arXiv

  21. [29]

    R. Aros, M. Contreras, R. Olea, R. Troncoso, and J. Zanelli, Conserved charges for gravity with locally AdS asymptotics, Phys. Rev. Lett.84, 1647 (2000), arXiv:gr-qc/9909015. 18

    2000 arXiv

  22. [30]

    R. Aros, M. Contreras, R. Olea, R. Troncoso, and J. Zanelli, Conserved charges for even dimensional asymptotically AdS gravity theories, Phys. Rev. D62, 044002 (2000), arXiv:hep-th/9912045

    2000 arXiv

  23. [31]

    Miskovic and R

    O. Miskovic and R. Olea, Topological regularization and self-duality in four-dimensional anti-de Sitter gravity, Phys. Rev. D 79, 124020 (2009), arXiv:0902.2082 [hep-th]

    2009 arXiv

  24. [32]

    Olea, Mass, angular momentum and thermodynamics in four-dimensional Kerr-AdS black holes, JHEP 06, 023, arXiv:hep-th/0504233

    R. Olea, Mass, angular momentum and thermodynamics in four-dimensional Kerr-AdS black holes, JHEP 06, 023, arXiv:hep-th/0504233

    arXiv

  25. [33]

    D. P. Sorokin, Introductory Notes on Non-linear Electrodynamics and its Applications, Fortsch. Phys.70, 2200092 (2022), arXiv:2112.12118 [hep-th]

    2022 arXiv

  26. [34]

    Bandos, K

    I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, A non-linear duality-invariant conformal extension of Maxwell’s equations, Phys. Rev. D102, 121703 (2020), arXiv:2007.09092 [hep-th]

    2020 arXiv

  27. [35]

    Tahamtan, Compatibility of nonlinear electrodynamics models with Robinson-Trautman geometry, Phys

    T. Tahamtan, Compatibility of nonlinear electrodynamics models with Robinson-Trautman geometry, Phys. Rev. D103, 064052 (2021), arXiv:2010.01689 [gr-qc]

    2021 arXiv

  28. [36]

    Kubiznak, T

    D. Kubiznak, T. Tahamtan, and O. Svitek, Slowly rotating black holes in nonlinear electrodynamics, Phys. Rev. D105, 104064 (2022), arXiv:2203.01919 [gr-qc]

    2022 arXiv

  29. [37]

    Bandos, K

    I. Bandos, K. Lechner, D. Sorokin, and P. K. Townsend, Nonlinear duality-invariant conformal extension of Maxwell’s equations, Phys. Rev. D102, 121703 (2020)

    2020

  30. [38]

    B. P. Kosyakov, Nonlinear electrodynamics with the maximum allowable symmetries, Phys. Lett. B810, 135840 (2020), arXiv:2007.13878 [hep-th]

    2020 arXiv

  31. [39]

    Barrientos, A

    J. Barrientos, A. Cisterna, D. Kubiznak, and J. Oliva, Accelerated black holes beyond Maxwell’s electrodynamics, Phys. Lett. B834, 137447 (2022), arXiv:2205.15777 [gr-qc]

    2022 arXiv

  32. [40]

    Flores-Alfonso, B

    D. Flores-Alfonso, B. A. González-Morales, R. Linares, and M. Maceda, Black holes and gravitational waves sourced by non-lineardualityrotation-invariantconformalelectromagneticmatter, Phys.Lett. B 812,136011(2021),arXiv:2011.10836 [gr-qc]

    2021 arXiv

  33. [41]

    Ballon Bordo, D

    A. Ballon Bordo, D. Kubizňák, and T. R. Perche, Taub-NUT solutions in conformal electrodynamics, Phys. Lett. B817, 136312 (2021), arXiv:2011.13398 [hep-th]

    2021 arXiv

  34. [42]

    Tahamtan, D

    T. Tahamtan, D. Flores-Alfonso, and O. Svitek, Well-posed nonvacuum solutions in Robinson-Trautman geometry, Phys. Rev. D108, 124076 (2023), arXiv:2311.03110 [gr-qc]

    2023 arXiv

  35. [43]

    Barrientos, A

    J. Barrientos, A. Cisterna, M. Hassaine, and K. Pallikaris, Electromagnetized black holes and swirling backgrounds in nonlinear electrodynamics: The ModMax case, Phys. Lett. B860, 139214 (2025), arXiv:2409.12336 [gr-qc]

    2025 arXiv

  36. [44]

    Bokulić and C

    A. Bokulić and C. A. R. Herdeiro, Exact multi-black hole spacetimes in Einstein-ModMax theory, (2025), arXiv:2501.04779 [gr-qc]

    2025 arXiv

  37. [45]

    T. Hale, D. Kubiznak, O. Svitek, and T. Tahamtan, Solutions and basic properties of regularized Maxwell theory, Phys. Rev. D107, 124031 (2023), arXiv:2303.16928 [gr-qc]

    2023 arXiv

  38. [46]

    T. Hale, D. Kubiznak, and J. Menšíková, Optical properties of black holes in regularized Maxwell theory, Phys. Rev. D 109, 084061 (2024), arXiv:2401.16259 [gr-qc]

    2024 arXiv

  39. [47]

    Abbasvandi, W

    N. Abbasvandi, W. Cong, D. Kubiznak, and R. B. Mann, Snapping swallowtails in accelerating black hole thermodynamics, Class. Quant. Grav.36, 104001 (2019), arXiv:1812.00384 [gr-qc]

    2019 arXiv

  40. [48]

    Ferrero, J

    P. Ferrero, J. P. Gauntlett, J. M. P. Ipiña, D. Martelli, and J. Sparks, Accelerating black holes and spinning spindles, Phys. Rev. D104, 046007 (2021), arXiv:2012.08530 [hep-th]

    2021 arXiv

  41. [49]

    Cassani, J

    D. Cassani, J. P. Gauntlett, D. Martelli, and J. Sparks, Thermodynamics of accelerating and supersymmetric AdS4 black holes, Phys. Rev. D104, 086005 (2021), arXiv:2106.05571 [hep-th]

    2021 arXiv

  42. [50]

    Boido, J

    A. Boido, J. P. Gauntlett, D. Martelli, and J. Sparks, Entropy Functions For Accelerating Black Holes, Phys. Rev. Lett. 130, 091603 (2023), arXiv:2210.16069 [hep-th]

    2023 arXiv

  43. [51]

    Ashtekar and S

    A. Ashtekar and S. Das, Asymptotically Anti-de Sitter space-times: Conserved quantities, Class. Quant. Grav.17, L17 (2000), arXiv:hep-th/9911230

    2000 arXiv

  44. [52]

    Kastor, S

    D. Kastor, S. Ray, and J. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav.26, 195011 (2009), arXiv:0904.2765 [hep-th]

    2009 arXiv

  45. [53]

    Kubiznak, R

    D. Kubiznak, R. B. Mann, and M. Teo, Black hole chemistry: thermodynamics with Lambda, Class. Quant. Grav.34, 063001 (2017), arXiv:1608.06147 [hep-th]

    2017 arXiv

  46. [54]

    Abbasvandi, W

    N. Abbasvandi, W. Ahmed, W. Cong, D. Kubizňák, and R. B. Mann, Finely Split Phase Transitions of Rotating and Accelerating Black Holes, Phys. Rev. D100, 064027 (2019), arXiv:1906.03379 [gr-qc]

    2019 arXiv

  47. [55]

    Ciambelli, C

    L. Ciambelli, C. Corral, J. Figueroa, G. Giribet, and R. Olea, Topological Terms and the Misner String Entropy, Phys. Rev. D103, 024052 (2021), arXiv:2011.11044 [hep-th]

    2021 arXiv

  48. [56]

    Corral and R

    C. Corral and R. Olea, Electric-magnetic duality of dyonic Kerr-Newman-NUT-AdS spacetimes, Phys. Rev. D110, 104021 (2024), arXiv:2408.03901 [hep-th]

    2024 arXiv

  49. [57]

    G. W. Gibbons and S. W. Hawking, Classification of Gravitational Instanton Symmetries, Commun. Math. Phys.66, 291 (1979)

    1979

  50. [58]

    Eguchi, P

    T. Eguchi, P. B. Gilkey, and A. J. Hanson, Gravitation, Gauge Theories and Differential Geometry, Phys. Rept.66, 213 (1980)

    1980

  51. [59]

    R. B. Mann, Misner string entropy, Phys. Rev. D60, 104047 (1999), arXiv:hep-th/9903229

    1999 arXiv

  52. [60]

    S. W. Hawking and S. F. Ross, Duality between electric and magnetic black holes, Phys. Rev. D52, 5865 (1995), arXiv:hep- th/9504019

    1995

  53. [61]

    Arenas-Henriquez, A

    G. Arenas-Henriquez, A. Cisterna, F. Diaz, and R. Gregory, Accelerating Black Holes in2 + 1dimensions: Holography revisited, JHEP09, 122, arXiv:2308.00613 [hep-th]. 19

    arXiv

  54. [62]

    Cisterna, F

    A. Cisterna, F. Diaz, R. B. Mann, and J. Oliva, Exploring accelerating hairy black holes in 2+1 dimensions: the asymptotically locally anti-de Sitter class and its holography, JHEP11, 073, arXiv:2309.05559 [hep-th]

    arXiv

  55. [63]

    Arenas-Henriquez, F

    G. Arenas-Henriquez, F. Diaz, and D. Rivera-Betancour, Generalized Fefferman-Graham gauge and boundary Weyl structures, (2024), arXiv:2411.12513 [hep-th]

    2024 arXiv

  56. [64]

    Elgood, P

    Z. Elgood, P. Meessen, and T. Ortín, The first law of black hole mechanics in the Einstein-Maxwell theory revisited, JHEP 09, 026, arXiv:2006.02792 [hep-th]

    2006 arXiv

  57. [65]

    G. W. Gibbons, M. J. Perry, and C. N. Pope, The First law of thermodynamics for Kerr-anti-de Sitter black holes, Class. Quant. Grav.22, 1503 (2005), arXiv:hep-th/0408217

    2005 arXiv

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