Near-horizon geometry with torsion: Kerr-AdS black hole

B. Cvetkovi\'c; D. Rakonjac

REVIEW 3 major objections 5 minor 28 references

Extremal Kerr-AdS black holes can carry non-trivial torsion with a smooth near-horizon limit, and this paper constructs the covariant conditions and a concrete solution.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

T0 review · deepseek-v4-flash

2026-08-03 21:27 UTC pith:5HXR5MBI

load-bearing objection Near-horizon construction is a real advance; the black-hole solution is a candidate that needs either explicit verification or a softer claim. the 3 major comments →

arxiv 2511.15106 v1 pith:5HXR5MBI submitted 2025-11-19 gr-qc

Near-horizon geometry with torsion: Kerr-AdS black hole

B. Cvetkovi\'c , D. Rakonjac This is my paper

classification gr-qc MSC 83C5783D0583C47 PACS 04.70.-s04.50.Kd

keywords near-horizon limittorsionKerr-AdSextremal black holePoincaré gauge theorydouble dualityNHEK-AdSRiemann-Cartan geometry

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper tries to extend the standard near-horizon geometry construction from the metric alone to spacetimes with torsion. It derives covariant conditions that a torsion tensor must satisfy to have a regular near-horizon limit at a degenerate Killing horizon, and shows that the known Kerr-AdS solution with dynamical torsion fails these conditions—its torsion diverges in the extremal limit. The paper then uses the near-horizon symmetry SL(2,R)×U(1), together with the double-duality method in Poincaré gauge theory, to construct a non-trivial torsion field on the NHEK-AdS metric that satisfies the conditions. It further claims that this near-horizon torsion is the limit of a new Kerr-AdS black hole solution with torsion, given by an explicit ansatz. If correct, this opens a path to entropies of extremal black holes with torsion in a sector of Poincaré gauge theory.

Core claim

The central discovery is a set of covariant geometric conditions—equation (2.8)—that a torsion tensor must obey at a degenerate Killing horizon to admit a smooth near-horizon limit. These conditions restrict the induced torsion on the horizon cross-section and its transverse derivative. The paper then constructs an explicit, non-trivial torsion solution on the NHEK-AdS metric, using an ansatz that respects the full near-horizon symmetry and the double-duality method to reduce the field equations. Finally, it presents a stationary, axisymmetric Kerr-AdS black hole ansatz with torsion that reduces to this near-horizon solution in the extremal limit, thereby claiming the first known example of

What carries the argument

The key machinery consists of three elements: (i) Gaussian null coordinates and the near-horizon scaling (2.3), which expose which torsion components diverge and lead to the covariant conditions (2.8); (ii) the near-horizon symmetry ansatz for torsion, derived from the Killing vectors of NHEK-AdS, which reduces the eight independent torsion functions to functions of θ; and (iii) the double-duality method, which converts the full Poincaré gauge field equations into simpler Einstein-like equations plus algebraic constraints on irreducible curvature and torsion components. The double-duality constraints also fix the Lagrangian sector, leaving a tractable system of differential equations for the

Load-bearing premise

The ansatz (6.2) with Ψ(r,θ) from (6.4) is assumed to be an actual solution of the full Poincaré gauge field equations once the double-duality constraints (6.11) are imposed; the paper defers a comprehensive analysis of this solution.

What would settle it

Compute the full PG field equations (3.3) for the ansatz (6.2) with Ψ from (6.4) and verify that every independent component is identically satisfied; if any component fails, the claimed black hole solution does not exist. A simpler check is to confirm that the near-horizon limit of this black hole torsion reproduces (6.1) with c(r+) = 0.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

The covariant conditions (2.8) give a quick diagnostic to test any black hole solution with torsion for the existence of a smooth near-horizon limit.
A well-defined near-horizon geometry with non-trivial torsion is now available in Poincaré gauge theory, enabling entropy computations via the canonical near-horizon analysis.
The new black hole solution provides a concrete example where the near-horizon limit commutes with the lift: the limit of the black hole torsion reproduces the near-horizon torsion.
The sector restrictions (6.11) identify a specific subspace of Lagrangian parameters where the solution lives, distinct from the sector of the previously known Kerr-AdS solution with torsion.
The method can be applied to other extremal black hole solutions in PG theories to search for regular near-horizon limits with torsion.

Where Pith is reading between the lines

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

The paper leaves unexplored the branches where Ψ3 and Ψ4 are both non-zero; these may yield further regular near-horizon torsions with different sectors.
If the black hole solution is confirmed, it would provide a testbed for Kerr/CFT-type entropy counting in theories with torsion, connecting classical near-horizon geometry to quantum gravity proposals.
The arbitrary function c(r) in (6.4) suggests a family of black holes with the same metric but different torsion; if c(r) is genuinely free, it would be an interesting degeneracy worth exploring.
The covariant conditions (2.8) might be reinterpreted as a form of extremality for torsion, analogous to the vanishing surface gravity for the metric, which could deepen the understanding of extremality in Riemann-Cartan geometry.

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

Near-horizon construction is a real advance; the black-hole solution is a candidate that needs either explicit verification or a softer claim.

read the letter

Here are the two things to know. First, the covariant near-horizon conditions for torsion and the explicit NHEK-AdS torsion solution are real new results. Second, the "new black hole solution" in Section 6 is a candidate, not a proven solution: the paper gives the necessary double-duality sector conditions but never substitutes the ansatz back into the full field equations.

The paper has a genuinely useful core. It identifies a real pathology — most PG black holes with dynamical torsion have divergent near-horizon torsion — and gives covariant criteria for when that does not happen. The closed-form near-horizon solution (5.8) is nontrivial and the sector analysis is competent. The lift to the black hole ansatz is clever, and the limiting procedure by design reproduces the near-horizon solution. If you work on near-horizon entropy in PG, this is a solid step forward.

The soft spots are the same ones the reader flagged. Section 6 never checks (6.2) against the full equations (3.3a,b). It computes curvature components and writes down the sector (6.11), which are necessary conditions coming from the double-duality ansatz. For a reader who accepts the double-duality theorem, the gap is probably bridgeable: one can read off ζ and χ from (4.9) and confirm that (4.7) and (4.8) hold. But the paper does not show that chain, and it leaves an arbitrary function c(r) in the candidate. The authors' own Section 7 says the solution "warrants a comprehensive analysis." That is honest, but it undercuts the claim in Section 6 that "we have obtained" a black hole solution.

There are also minor but real typesetting issues in the main covariant conditions (2.8) — at least one index contraction is clearly wrong. That needs fixing before the general criteria can be used with confidence. The match between the lifted Ψ(r,θ) and the near-horizon Ψ(θ) is built into the ansatz, so the "demonstration" in the abstract should be read as construction-by-design, not independent verification.

Bottom line: the near-horizon contribution deserves a serious referee and likely publication after revision. The black-hole part should be either verified or explicitly labeled a candidate. I would send it to peer review.

Referee Report

3 major / 5 minor

Summary. The paper develops covariant conditions for the existence of a regular near-horizon limit for extremal black holes with non-zero torsion in Poincaré gauge theory (PG). After showing that a known Kerr-AdS black hole with dynamical torsion fails these conditions, the authors construct a near-horizon solution for the NHEK-AdS metric using a symmetry ansatz for the torsion and the double-duality method. They solve the degenerate branch Ψ_3=Ψ_4=0, obtain a torsion function Ψ(θ), and derive the corresponding Lagrangian parameter sector. They then propose a black-hole ansatz with the same torsion structure, setting Ψ(r,θ) by requiring constant Ricci scalar, and claim to have obtained an extremal Kerr-AdS black hole with torsion that has a regular near-horizon limit. The paper also discusses the interpretation of the near-horizon conditions and outlines future work.

Significance. If the central existence claim is established, the paper would provide a concrete example of an extremal black hole with dynamical torsion having a well-defined near-horizon geometry, filling a gap identified in earlier PG entropy calculations. The covariant conditions for a regular near-horizon torsion limit, if correct, are a useful general result. The use of the double-duality method and the explicit construction are potentially valuable for further studies of extremal black holes in PG. However, the main claim rests on an incomplete verification: the black-hole ansatz is not shown to satisfy the full PG field equations, and the paper itself defers that analysis to future work. The paper also contains a likely typo in one of the central covariant conditions.

major comments (3)

[§6, Eqs. (6.2)–(6.4), (6.11)] The central claim that Eq. (6.2) with Ψ(r,θ) given by Eq. (6.4) is a Kerr-AdS black hole solution of PG is not verified. The paper imposes constant Ricci scalar and then computes irreducible curvature/torsion components, from which the sector relations (6.11) are read off. However, it is never shown that the double-duality relation (4.7) holds with explicit ζ and χ, nor that the full field equations (3.3a,b) are satisfied. The authors themselves state in §7 that the black-hole solution 'warrants a comprehensive analysis' and leave it for future work. Without this verification, the statement 'We have now obtained a Kerr-AdS black hole...' is not supported by the calculations shown.
[§6, Eq. (6.4)] The undetermined function c(r) in Ψ(r,θ) is left arbitrary. If the ansatz is a solution for every c(r), this is a large functional freedom that must be either fixed by boundary conditions, shown to be pure gauge, or explicitly verified against the field equations. If c(r) is not arbitrary, the condition that selects it is not given. The paper only notes that the 'actual solution of interest' may have c(r)=0, which is insufficient for the existence claim.
[§2.2, Eq. (2.8)] The first covariant condition as typeset, T_{\mu\nu\rho} k^\mu k^\nu = 0, is identically zero by the antisymmetry of the torsion tensor in μ,ν. The intended physical condition (e.g., vanishing of the torsion current along the horizon generators, as discussed in the text) is therefore misstated. Since these conditions are a primary result of the paper and are used to characterize regular near-horizon torsion, the correct covariant form must be provided and the conditions should be checked for the constructed solutions.

minor comments (5)

[§3.1] The claim that the near-horizon limit of torsion diverges for the Baekler et al. solution is argued heuristically via singular Lorentz transformations. A more explicit computation or a direct verification using the conditions (2.8) would be clearer.
[§5] The text states that Ψ_3=0 implies Ψ_4=0 and vice versa, and only the degenerate branch is solved. This is a self-acknowledged limitation, but the non-degenerate branch deserves at least a comment on its physical relevance or intractability.
[Eqs. (5.6), (6.3)] The Ricci scalar is set to R=12λ, whereas for the standard Kerr-AdS metric one usually has R=-12λ (with λ=1/ℓ²). The sign convention should be clarified, since this affects the identification of the Lagrangian sector.
[Various] There are several typographical issues: 'neccessary' in §2.1, 'Cimmmento' in ref. [23], 'Kerr-Newmann' in ref. [24], and inconsistent notation for Ψ in Eqs. (5.8) and (6.4).
[§4.1] The double-duality method is summarized concisely, but the derivation of the reduced field equations (4.8) is referenced rather than shown. A fuller explanation or a pointer to the exact equations in the cited literature would improve reproducibility.

Circularity Check

1 steps flagged

Near-horizon match is built into the ansatz by solving the same constant-Ricci-scalar ODE; full PG equations remain unchecked.

specific steps

self definitional [Section 6, eqs. (6.3)-(6.4) vs Section 5, eqs. (5.7)-(5.8)]
""Since we managed to set Ricci scalar to constant, and that torsion in fact correctly corresponds to the one found in section 5 after taking the near-horizon limit, we proceed to calculate other irreducible torsion and curvature components. ... We see that what appeared before as the integration constant is now an arbitrary function of radial coordinate c(r).""

The black-hole torsion function (6.4) is the general solution of the same ODE (6.3) with R=12\lambda that was already solved in (5.7)-(5.8) for the near-horizon function, with the integration constant promoted to c(r). Therefore Psi(r,theta)|_{r=r+} equals Psi_1(theta) identically, so the asserted 'correct correspondence' of the near-horizon limit is not an independent check but is fixed by the choice of ansatz. The later claim 'We have now obtained a Kerr-AdS black hole ... which has a regular near-horizon limit' inherits this construction-by-design, and the full PG equations are not shown to be satisfied.

full rationale

The Section 2 covariant near-horizon conditions and the double-duality reduction are not circular: they are derived from scaling behavior and from independent external methods [29,30], and the near-horizon solution is obtained within the reduced system. Self-citations are not load-bearing for the central derivation. The only exhibited circularity is in Section 6: the black-hole torsion Psi(r,theta) is chosen as the general solution of the same constant-Ricci-scalar equation (6.3) that defined the near-horizon function Psi_1 in (5.7)-(5.8), with the integration constant promoted to c(r). Hence the restriction Psi(r,theta)|_{r=r+} equals Psi_1(theta) by construction, so the claimed near-horizon correspondence is built into the ansatz rather than tested independently. I also flag, per the reviewing rule, the authors' own admission that the black hole solution 'warrants a comprehensive analysis' and is 'left for future studies'; the full PG equations (3.3) are never substituted and checked, which is a completeness/correctness gap rather than a circularity. Score 4 reflects one construction-by-design correspondence while the rest of the derivation retains independent content.

Axiom & Free-Parameter Ledger

1 free parameters · 7 axioms · 0 invented entities

The central construction rests on the double-duality reduction and on symmetry/determinacy assumptions. The most expensive input is the ad hoc assumption that torsion has the full SL(2,R)×U(1) symmetry, and the least-supported step is treating the black-hole ansatz as a field-equation solution without explicit verification. c(r) is an undetermined free function.

free parameters (1)

c(r) (also c in near-horizon solution) = arbitrary; c=0 selected for physical interest
Integration 'constant' in (5.8) and arbitrary radial function in (6.4); undetermined by field equations and acknowledged as likely unphysical.

axioms (7)

standard math Hawking rigidity: event horizons are Killing horizons.
Used in §2.1 to apply Killing-horizon construction to black hole horizons; cited [17–19].
domain assumption Torsion is analytic and regular in Gaussian null coordinates near the horizon.
Needed in §2.2 to read off component scaling and derive conditions (2.6).
domain assumption Near-horizon metric of extremal Kerr-AdS has SL(2,R)×U(1) symmetry group.
Inherited from GR near-horizon theorems [11,12]; used in §4 to construct the torsion ansatz.
ad hoc to paper Torsion inherits the full SL(2,R)×U(1) symmetry, including the dynamically generated ξ4.
Assumed in §4; authors note this is not guaranteed by the limiting procedure and is model-dependent.
domain assumption Double-duality ansatz (4.7) reduces PG field equations to Einstein equation plus algebraic constraints (4.8)-(4.9).
Imported from [29,30]; this reduction is the basis for claiming the sector constraints produce a solution.
ad hoc to paper Degenerate branch Ψ3=Ψ4=0 covers the relevant solution space.
§5: the non-degenerate system is left unsolved; the solution is found only in the degenerate branch.
ad hoc to paper Black-hole ansatz (6.2) with Ψ(r,θ) satisfies the full field equations.
Asserted via sector analysis in §6, but not explicitly verified; the paper defers complete analysis to future work.

pith-pipeline@v1.3.0-alltime-deepseek · 15179 in / 16113 out tokens · 148464 ms · 2026-08-03T21:27:12.797925+00:00 · methodology

0 comments

read the original abstract

We consider the general construction of near-horizon limit for extremal black hole solutions with non-trivial torsion, and derive the covariant geometric conditions for the existence this limit. A near-horizon solution with torsion is constructed in the case of extremal Kerr-AdS black hole, starting from an ansatz compatible with near-horizon symmetry. We demonstrate that this solution corresponds to the limit of a new black hole solution with torsion.

discussion (0)

Reference graph

Works this paper leans on

28 extracted references · 15 linked inside Pith

[1]

Blagojević and B

M. Blagojević and B. Cvetković, Entropy in Poincaré gauge theory: Hamiltonian ap- proach, Phys. Rev. D99(2019) 10, 104058, [arXiv:1903.02263]

Pith/arXiv arXiv 2019
[2]

R. M. Wald, Black hole entropy is a Noether charge, Phys. Rev. D48(1993) R3427- R3431, [arXiv:9307038]; R. M. Wald, The thermodynamics of black holes, Living Rev. Relativity4(2001) 6, doi:10.12942/lrr-2001-6 (44 pages), [arXiv:9912119]

doi:10.12942/lrr-2001-6 1993
[3]

Blagojević and Cvetković, Hamiltonian approach to black hole entropy: Kerr-like spacetimes, Phys

M. Blagojević and Cvetković, Hamiltonian approach to black hole entropy: Kerr-like spacetimes, Phys. Rev. D100(2019) 4, 044029, [arXiv:1905.04928]

Pith/arXiv arXiv 2019
[4]

Blagojević and Cvetković, Entropy in general relativity: Kerr-AdS black hole, Phys

M. Blagojević and Cvetković, Entropy in general relativity: Kerr-AdS black hole, Phys. Rev. D101(2020) 8, 084023, [arXiv:2002.05029]; M. Blagojević and Cvetković, Entropy in Poincaré gauge theory: Kerr-AdS solution, Phys. Rev. D102(2020) 6, 064034, [arXiv:2007.10721]

Pith/arXiv arXiv 2020
[5]

Blagojević and Cvetković, Entropy of Reissner-Nordström-like black holes, Phys

M. Blagojević and Cvetković, Entropy of Reissner-Nordström-like black holes, Phys. Lett. B824(2022) 136815 (5 pages) [arXiv:2112.02099]

Pith/arXiv arXiv 2022
[6]

Blagojević and Cvetković, Entropy of Kerr-Newmann-AdS black holes with torsion, Phys

M. Blagojević and Cvetković, Entropy of Kerr-Newmann-AdS black holes with torsion, Phys. Rev. D105(2022) 10, 104014 [arXiv:2203.14696]

Pith/arXiv arXiv 2022
[8]

Compère, The Kerr/CFT correspondence and its Extensions

G. Compère, The Kerr/CFT correspondence and its Extensions. Living Rev. Relativity 15(2012) 11, doi:10.12942/lrr-2012-11 (81 pages), [arXiv:0809.4266]

Pith/arXiv arXiv 2012
[9]

Carlip, Effective conformal descriptions of black hole entropy, Entropy13(2011), 1355-1379, [arXiv:1107.2678]

S. Carlip, Effective conformal descriptions of black hole entropy, Entropy13(2011), 1355-1379, [arXiv:1107.2678]

Pith/arXiv arXiv 2011
[10]

Bardeen and G

J. Bardeen and G. T. Horowitz, The Extreme Kerr Throat Geometry: A Vacuum Analog ofAdS 2 ×S 2, Phys. Rev. D6010, 104030 (1999), [arXiv:hep-th/9905099]

Pith/arXiv arXiv 1999
[11]

H. K. Kunduri, J. Lucietti and H. S. Reall, Near-horizon symmetries of extremal black holes, Class. Quantum Grav.24(2007) 16, 4169, [arXiv:0705.4214]

Pith/arXiv arXiv 2007
[12]

H. K. Kunduri and J. Lucietti, Classification of near-horizon geometries of extremal black holes, Living Rev. Relativity16(2013) 8, [arXiv:1306.2517]

Pith/arXiv arXiv 2013
[13]

Cvetković and D

B. Cvetković and D. Rakonjac, Extremal Kerr black hole entropy in Poincaré gauge theory, Phys.Rev. D107(2023) 4, 044054, [arXiv:2208.04383]

Pith/arXiv arXiv 2023
[14]

Cvetković and D

B. Cvetković and D. Rakonjac, Near horizon symmetry of extremal spacelike-stretched black holes, Phys. Rev. D109(2024) 12, 124043, [arXiv:2403.08529]

Pith/arXiv arXiv 2024
[15]

Friedrich, I

H. Friedrich, I. Rácz and R. M. Wald, On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon, Commun. Math. Phys.204, 691–707 (1999), [arXiv:gr-qc/9811021]. 18

Pith/arXiv arXiv 1999
[16]

Moncrief and J

V. Moncrief and J. Isenberg, Symmetries of Cosmological Cauchy Horizons, Commun. Math. Phys.89, 387–413 (1983)

1983
[17]

Hawking, Black holes in general relativity, Commun

S.W. Hawking, Black holes in general relativity, Commun. Math. Phys.25, 152-166 (1972)

1972
[18]

Hawking and G.F.R

S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press (1973)

1973
[19]

Chruściel, On rigidity of analytic black holes, Commun

P.T. Chruściel, On rigidity of analytic black holes, Commun. Math. Phys.189, 1-7 (1997)

1997
[20]

R. Dey, S. Liberati, and D. Pranzetti, Spacetime thermodynamics in the presence of torsion, Phys. Rev. D96(2017) 12, 124032, [arXiv:1709.04031]

Pith/arXiv arXiv 2017
[21]

Blagojević,Gravitation and Gauge Symmetries(IoP, Bristol, 2002)

M. Blagojević,Gravitation and Gauge Symmetries(IoP, Bristol, 2002). [22]Gauge Theories of Gravitation, A Reader with Commentaries, edited by M. Blagojević and F. W. Hehl (Imperial College Press, London, 2013)

2002
[23]

J. D. McCrea, P. Baekler and M. Gürses, A Kerr-like solution of the Poincaré gauge field equations, Nuovo Cimmento 99B(1987) 171–177

1987
[24]

Baekler, M

P. Baekler, M. Gürses, F. W. Hehl, and J. D. McCrea, The exterior gravitational field of a charges spinning source in the Poincaré gauge theory: a Kerr-Newmann metric with dynamic torsion, Phys. Lett. A128(1988) 245–250

1988
[25]

Carter, Black hole equilibrium states, inBlack holes, 1972 Les Houches Lectures, edited by C

B. Carter, Black hole equilibrium states, inBlack holes, 1972 Les Houches Lectures, edited by C. DeWitt and B. S. DeWitt (Gordon and Breach, New York, 1973) pp. 58-214

1972
[26]

Geroch, Limits of spacetimes

R. Geroch, Limits of spacetimes. Commun. Math. Phys.13, 180–193 (1969)

1969
[27]

J. A. R. Cembranos and J. G. Valcarcel, New torsion black hole solutions in Poincaré gauge theory, J. Cosmol. Astropart. Phys.01, 014 (2017) [arXiv:1608.00062]

Pith/arXiv arXiv 2017
[28]

Rauch and H

R. Rauch and H. T. Nieh, Birkhoff’s theorem for general Riemann-Cartan-typeR+R2 theories of gravity, Phys. Rev. D24(1981) 8, 2029-2048

1981
[29]

Yu. N. Obukhov, Poincaré gauge gravity: Selected topics, Int. J. Geom. Methods Mod. Phys.03(2006) 95-138

2006
[30]

Zhytnikov, Double duality and hidden gauge freedom in the Poincaré gauge theory of gravitation, Gen

V.V. Zhytnikov, Double duality and hidden gauge freedom in the Poincaré gauge theory of gravitation, Gen. Rel. Grav.28(1996) 137-162. 19

1996

[1] [1]

Blagojević and B

M. Blagojević and B. Cvetković, Entropy in Poincaré gauge theory: Hamiltonian ap- proach, Phys. Rev. D99(2019) 10, 104058, [arXiv:1903.02263]

Pith/arXiv arXiv 2019

[2] [2]

R. M. Wald, Black hole entropy is a Noether charge, Phys. Rev. D48(1993) R3427- R3431, [arXiv:9307038]; R. M. Wald, The thermodynamics of black holes, Living Rev. Relativity4(2001) 6, doi:10.12942/lrr-2001-6 (44 pages), [arXiv:9912119]

doi:10.12942/lrr-2001-6 1993

[3] [3]

Blagojević and Cvetković, Hamiltonian approach to black hole entropy: Kerr-like spacetimes, Phys

M. Blagojević and Cvetković, Hamiltonian approach to black hole entropy: Kerr-like spacetimes, Phys. Rev. D100(2019) 4, 044029, [arXiv:1905.04928]

Pith/arXiv arXiv 2019

[4] [4]

Blagojević and Cvetković, Entropy in general relativity: Kerr-AdS black hole, Phys

M. Blagojević and Cvetković, Entropy in general relativity: Kerr-AdS black hole, Phys. Rev. D101(2020) 8, 084023, [arXiv:2002.05029]; M. Blagojević and Cvetković, Entropy in Poincaré gauge theory: Kerr-AdS solution, Phys. Rev. D102(2020) 6, 064034, [arXiv:2007.10721]

Pith/arXiv arXiv 2020

[5] [5]

Blagojević and Cvetković, Entropy of Reissner-Nordström-like black holes, Phys

M. Blagojević and Cvetković, Entropy of Reissner-Nordström-like black holes, Phys. Lett. B824(2022) 136815 (5 pages) [arXiv:2112.02099]

Pith/arXiv arXiv 2022

[6] [6]

Blagojević and Cvetković, Entropy of Kerr-Newmann-AdS black holes with torsion, Phys

M. Blagojević and Cvetković, Entropy of Kerr-Newmann-AdS black holes with torsion, Phys. Rev. D105(2022) 10, 104014 [arXiv:2203.14696]

Pith/arXiv arXiv 2022

[7] [8]

Compère, The Kerr/CFT correspondence and its Extensions

G. Compère, The Kerr/CFT correspondence and its Extensions. Living Rev. Relativity 15(2012) 11, doi:10.12942/lrr-2012-11 (81 pages), [arXiv:0809.4266]

Pith/arXiv arXiv 2012

[8] [9]

Carlip, Effective conformal descriptions of black hole entropy, Entropy13(2011), 1355-1379, [arXiv:1107.2678]

S. Carlip, Effective conformal descriptions of black hole entropy, Entropy13(2011), 1355-1379, [arXiv:1107.2678]

Pith/arXiv arXiv 2011

[9] [10]

Bardeen and G

J. Bardeen and G. T. Horowitz, The Extreme Kerr Throat Geometry: A Vacuum Analog ofAdS 2 ×S 2, Phys. Rev. D6010, 104030 (1999), [arXiv:hep-th/9905099]

Pith/arXiv arXiv 1999

[10] [11]

H. K. Kunduri, J. Lucietti and H. S. Reall, Near-horizon symmetries of extremal black holes, Class. Quantum Grav.24(2007) 16, 4169, [arXiv:0705.4214]

Pith/arXiv arXiv 2007

[11] [12]

H. K. Kunduri and J. Lucietti, Classification of near-horizon geometries of extremal black holes, Living Rev. Relativity16(2013) 8, [arXiv:1306.2517]

Pith/arXiv arXiv 2013

[12] [13]

Cvetković and D

B. Cvetković and D. Rakonjac, Extremal Kerr black hole entropy in Poincaré gauge theory, Phys.Rev. D107(2023) 4, 044054, [arXiv:2208.04383]

Pith/arXiv arXiv 2023

[13] [14]

Cvetković and D

B. Cvetković and D. Rakonjac, Near horizon symmetry of extremal spacelike-stretched black holes, Phys. Rev. D109(2024) 12, 124043, [arXiv:2403.08529]

Pith/arXiv arXiv 2024

[14] [15]

Friedrich, I

H. Friedrich, I. Rácz and R. M. Wald, On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon, Commun. Math. Phys.204, 691–707 (1999), [arXiv:gr-qc/9811021]. 18

Pith/arXiv arXiv 1999

[15] [16]

Moncrief and J

V. Moncrief and J. Isenberg, Symmetries of Cosmological Cauchy Horizons, Commun. Math. Phys.89, 387–413 (1983)

1983

[16] [17]

Hawking, Black holes in general relativity, Commun

S.W. Hawking, Black holes in general relativity, Commun. Math. Phys.25, 152-166 (1972)

1972

[17] [18]

Hawking and G.F.R

S.W. Hawking and G.F.R. Ellis, The large scale structure of space-time, Cambridge University Press (1973)

1973

[18] [19]

Chruściel, On rigidity of analytic black holes, Commun

P.T. Chruściel, On rigidity of analytic black holes, Commun. Math. Phys.189, 1-7 (1997)

1997

[19] [20]

R. Dey, S. Liberati, and D. Pranzetti, Spacetime thermodynamics in the presence of torsion, Phys. Rev. D96(2017) 12, 124032, [arXiv:1709.04031]

Pith/arXiv arXiv 2017

[20] [21]

Blagojević,Gravitation and Gauge Symmetries(IoP, Bristol, 2002)

M. Blagojević,Gravitation and Gauge Symmetries(IoP, Bristol, 2002). [22]Gauge Theories of Gravitation, A Reader with Commentaries, edited by M. Blagojević and F. W. Hehl (Imperial College Press, London, 2013)

2002

[21] [23]

J. D. McCrea, P. Baekler and M. Gürses, A Kerr-like solution of the Poincaré gauge field equations, Nuovo Cimmento 99B(1987) 171–177

1987

[22] [24]

Baekler, M

P. Baekler, M. Gürses, F. W. Hehl, and J. D. McCrea, The exterior gravitational field of a charges spinning source in the Poincaré gauge theory: a Kerr-Newmann metric with dynamic torsion, Phys. Lett. A128(1988) 245–250

1988

[23] [25]

Carter, Black hole equilibrium states, inBlack holes, 1972 Les Houches Lectures, edited by C

B. Carter, Black hole equilibrium states, inBlack holes, 1972 Les Houches Lectures, edited by C. DeWitt and B. S. DeWitt (Gordon and Breach, New York, 1973) pp. 58-214

1972

[24] [26]

Geroch, Limits of spacetimes

R. Geroch, Limits of spacetimes. Commun. Math. Phys.13, 180–193 (1969)

1969

[25] [27]

J. A. R. Cembranos and J. G. Valcarcel, New torsion black hole solutions in Poincaré gauge theory, J. Cosmol. Astropart. Phys.01, 014 (2017) [arXiv:1608.00062]

Pith/arXiv arXiv 2017

[26] [28]

Rauch and H

R. Rauch and H. T. Nieh, Birkhoff’s theorem for general Riemann-Cartan-typeR+R2 theories of gravity, Phys. Rev. D24(1981) 8, 2029-2048

1981

[27] [29]

Yu. N. Obukhov, Poincaré gauge gravity: Selected topics, Int. J. Geom. Methods Mod. Phys.03(2006) 95-138

2006

[28] [30]

Zhytnikov, Double duality and hidden gauge freedom in the Poincaré gauge theory of gravitation, Gen

V.V. Zhytnikov, Double duality and hidden gauge freedom in the Poincaré gauge theory of gravitation, Gen. Rel. Grav.28(1996) 137-162. 19

1996