Pith. sign in

REVIEW 3 major objections 4 minor 68 references

Extended Near Horizon Symmetries of Extremal BTZ Black Holes in 3D Massive Gravity

T0 review · 3 major / 4 minor · reviewed 2026-08-11 · deepseek-v4-flash

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

Pith's one-line read Near-horizon extremal BTZ black holes in New Massive Gravity and Topological Massive Gravity carry two centrally extended Virasoro algebras whose central charges match the spatial-infinity values.

desk verdict A careful higher-derivative extension of the non-chiral Kerr/CFT computation; the central charges match, but the regularization's limit-ordering remains the load-bearing assumption. read the letter →

arxiv 2412.18286 v3 pith:EHZW3AAQ submitted 2024-12-24 hep-th

Debojyoti Ballav , Shailesh Kulkarni This is my paper · ORCID
classification hep-th
keywords near-horizonextremalBTZNewMassiveGravityTopologicalVirasoroalgebracentralchargeasymptoticsymmetryhigher-derivativeboundaryconditions
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 aims to establish that the near-horizon region of an extremal BTZ black hole in three-dimensional massive gravity supports two copies of the Virasoro algebra, each with a nonzero central charge. In the standard near-horizon treatment only the left-moving sector acquires a central charge, because the conformal boundary of the near-horizon metric is null and the charge integral on equal-time surfaces degenerates there. The authors impose a non-chiral boundary condition that allows diffeomorphisms depending on both a time function and an angular function, and they evaluate the conserved charges on a deformed metric obtained by the coordinate change $t' = t + \beta \phi$, $\phi' = \phi$. The deformation makes the boundary spacelike and activates the right-moving central charge, giving $c_L = c_R$ for New Massive Gravity and unequal $c_L$ and $c_R$ for Topological Massive Gravity. These values agree with the known asymptotic central charges at spatial infinity, so the near-horizon calculation reproduces the full two-Virasoro structure of the dual CFT.

What carries the argument

The machinery is the non-chiral boundary condition, which permits asymptotic Killing vectors built from two arbitrary functions, $\tau(t)$ in the time direction and $\epsilon(\phi)$ in the angular direction, together with the linear deformation $t' = t + \beta\phi$, $\phi' = \phi$. The deformation changes the conformal-boundary metric from the degenerate form $-dt\,d\phi$ to the positive-definite form $2\beta r\,d\phi^2$, and it mixes the components of the covariant phase-space charge 2-form through $\tilde{k}^{t'r'} = k^{tr} + \beta k^{\phi r}$. The coefficient of the $p^3$ term in the integrated charge yields the central charge.

What would settle it

Recompute the right-moving central charge on the deformed metric with the limits taken in the opposite order, $\beta\to0$ before $r\to\infty$; if the result is $c_R=0$, or if an independent spacelike-slice calculation on the original metric gives a different nonzero $c_R$, the claimed central charge is a product of the regularization rather than a property of the near-horizon geometry.

Watch

Extended reading notes

Core claim

The central discovery is that the vanishing of the right-moving central charge in the original near-horizon coordinates is a boundary artifact, not a property of the theory. In those coordinates the equal-time surface becomes null at the conformal boundary, so the $(t,r)$ component of the charge integrand for right-moving diffeomorphisms falls as $O(r^{-3})$ for New Massive Gravity or $O(r^{-2})$ for Topological Massive Gravity and integrates to zero. After the deformation $t' = t + \beta \phi$, $\phi' = \phi$, the charge 2-form transforms as $\tilde{k}^{t'r'} = k^{tr} + \beta k^{\phi r}$; the $(\phi,r)$ component, which is nonzero for right-movers, supplies the missing $p^3$ terms. The integrated charges then obey two centrally extended Virasoro algebras, with $c_L = c_R = \frac{3\ell}{2G_3}\left(1 - \frac{1}{2m^2\ell^2}\right)$ for New Massive Gravity and $c_L = \frac{3\ell}{2G_3}\left(1 + \frac{1}{\mu\ell}\right)$, $c_R = \frac{3\ell}{2G_3}\left(1 - \frac{1}{\mu\ell}\right)$ for Topological Massive Gravity, exactly matching the spatial-infinity values.

Load-bearing premise

The whole derivation of the right-moving central charge assumes that evaluating charges on the deformed metric with $r\to\infty$ taken before $\beta\to0$ recovers the charge algebra of the original null-boundary near-horizon geometry; if that order of limits is invalid, $c_R$ is a regularization artifact.

Editorial extensions

If this is right

  • For New Massive Gravity, the near-horizon central charges are $c_L = c_R = \frac{3\ell}{2G_3}\left(1 - \frac{1}{2m^2\ell^2}\right)$, reproducing the known spatial-infinity values, and the Cardy entropy computed from these charges matches the Wald entropy.
  • For Topological Massive Gravity, the same procedure gives $c_L = \frac{3\ell}{2G_3}\left(1 + \frac{1}{\mu\ell}\right)$ and $c_R = \frac{3\ell}{2G_3}\left(1 - \frac{1}{\mu\ell}\right)$, again matching the spatial-infinity results.
  • The left-moving central charge is unchanged by the deformation, while the right-moving one arises only after regularization; both are independent of the periodicity parameter and of the deformation parameter.
  • The Frolov-Thorne temperatures in both theories are $T_L = \eta/(2\pi\ell)$ and $T_R = 0$, consistent with the extremal limit and with a dual CFT in which only left movers are excited.
  • Applying the same deformation to asymptotically AdS$_3$ black holes with a spacelike boundary leaves the standard central charges unchanged, which the paper takes as evidence that the regularization procedure is robust.

Reading between the lines

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

  • The mixing relation $\tilde{k}^{t'r'} = k^{tr} + \beta k^{\phi r}$ suggests the regularization is a general property of the covariant phase-space charge potential, so analogous non-chiral extensions should exist for other three-dimensional higher-derivative theories admitting near-horizon extremal BTZ solutions, such as generalized minimal massive gravity or extended new massive gravity.
  • Because the deformed near-horizon metric is locally AdS$_3$, the two near-horizon Virasoro algebras may simply be the standard left/right Virasoro algebras of the AdS$_3$ boundary in near-horizon coordinates; if true, the non-chiral extension would be a relabeling of the known boundary symmetry rather than a newly discovered one.
  • The order-of-limits dependence can be tested directly: computing charges on the deformed metric with $\beta\to0$ before $r\to\infty$ should give $c_R=0$, which would mark the right-moving central charge as a regulator artifact rather than a geometric charge.
  • A logical next step is to compute the right-moving central charge for these theories by an independent method, such as a stretched-horizon or membrane approach; agreement with the regularized result would certify the prescription beyond the specific coordinate choice.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper studies the asymptotic symmetry algebra of near-horizon extremal BTZ (NHEBTZ) black holes in New Massive Gravity (NMG) and Topological Massive Gravity (TMG). Using the non-chiral boundary condition of Azeyanagi et al. and a coordinate-deformation regularization, the authors compute Barnich-Brandt-Compere surface charges and obtain two centrally extended Virasoro algebras with central charges c_L = c_R = (3ℓ/2G_3)(1 - 1/(2m²ℓ²)) for NMG and c_L = (3ℓ/2G_3)(1 + 1/(μℓ)), c_R = (3ℓ/2G_3)(1 - 1/(μℓ)) for TMG, matching the known spatial-infinity Brown-Henneaux values. They also relate the regularized generators to those of asymptotically AdS3 and compute the microscopic entropy via Cardy's formula.

Significance. If the regularization prescription is accepted, the paper provides a nontrivial extension of non-chiral near-horizon symmetry analysis from Einstein gravity to higher-derivative massive gravities, with explicit central charges that agree with independent spatial-infinity results. The use of the BBC formalism and the consistency checks (left-moving charges unaffected by deformation, entropy match) are strengths. However, the central claim's validity hinges on an order-of-limits prescription that is not independently justified for the original null-boundary NHEBTZ geometry.

major comments (3)
  1. [Section 2.2, Eqs. (2.24)-(2.29)] The nonzero right-moving central charge c_R is an artifact of the order of limits r→∞ before β→0 on the deformed metric (2.25); the unregularized right-moving potential is O(1/r³) for NMG and O(1/r²) for TMG, the deformed generator (2.27b) has no smooth β→0 limit, and the t' period shrinks to zero with β. Since the paper claims this charge algebra for the NHEBTZ geometry itself, please justify this limiting order physically or explicitly restrict the claim to the deformed one-parameter family of regularized geometries.
  2. [Section 4, Eqs. (4.1)-(4.8)] The asymptotically AdS3 example demonstrates that the deformation does not change the central charges when the boundary is already spacelike, but this does not validate the r→∞-before-β→0 order for the null NHEBTZ boundary. A direct check, e.g., computing the charges in the opposite order or showing an ordering-independent definition, is needed to support the central claim.
  3. [Section 3, Eqs. (3.7a)-(3.7b)] The TMG analysis inherits the same regularization-order ambiguity as the NMG case; moreover, since c_R = (3ℓ/2G_3)(1 - 1/(μℓ)) can be negative for μℓ < 1, the authors should comment on whether the regularized right-moving sector is unitary or whether this is a known feature of TMG.
minor comments (4)
  1. [Eq. (2.10)] The displayed prefactor for C_{ξ_q,ξ_p} appears to be missing a division sign; please correct the typographical error.
  2. [Section 4, Eqs. (4.5)-(4.6)] The factor η is missing in ζ^-_p compared with Eq. (2.27b); please specify the coordinate scalings that relate the two generators.
  3. [Appendix A, Eq. (A.5)] The same symbols φ and τ are used for both old and new variables in the redefinition; please introduce new symbols to avoid confusion.
  4. [Eqs. (2.28)-(2.29) and (3.7a)-(3.7b)] The central extension computations are presented without intermediate steps; providing a supplementary Mathematica notebook or a sample derivation would help readers verify the results.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the two-Virasoro central charges are obtained by direct BBC computation from the (deformed) NHEBTZ metric and match independent spatial-infinity values; self-citations are corroborative only.

full rationale

No circular step is present; the score 2 reflects only the existence of minor, non-load-bearing self-citations. The central charges are not inserted into the derivation: Sections 2-3 compute the BBC potentials (2.28)-(2.29) and (3.7a)-(3.7b) directly from the NHEBTZ metric (2.3) and its relabeled form (2.25) using the standard covariant-phase-space formula (B.2), and the c-values (2.33) and (3.8) are read off the p^3 coefficients of those explicit potentials. Nothing is fitted: the only free parameters, the deformation parameter beta and the period alpha, drop out of the final charges, as the paper states below Eq. (2.33). The nontrivial right-moving charge arises because the relabeling t' = t + beta phi mixes the (t,r) and (phi,r) components of the BBC potential (k~ = k^{tr} + beta k^{phi r}, below Eq. (2.30)), a mechanism the paper states transparently in the conclusions. The outputs are then benchmarked against independent results: spatial-infinity Brown-Henneaux central charges ([55,56] for NMG, [34] for TMG) and the Wald entropy, so the comparison is externally anchored. Self-citations ([40], [53,54], [59]) only corroborate the chiral central charge the paper itself derives at (2.9)-(2.12), or provide standard formalism and mass formulas; none carries the central claim. The skeptic's concern that the nonzero c_R depends on the stated r->infinity-before-beta->0 ordering, and that the right-moving generators (2.27b) have no smooth beta->0 limit, is a physical-validity question about which foliation defines near-horizon charges, not a circularity: the regularization choices are fixed by boundary-metric positivity, g_{t't'}=0, and compactification (text below Eq. (2.23)), not by the target central charge.

Assumptions & free parameters 2 free parameters · 4 assumptions · 0 invented entities

The paper introduces no new entities or fitted physical constants. Its load-bearing inputs are the BBC charge formula from prior literature and the regularization prescription of [22]; these are assumptions the reader must grant.

free parameters (2)
  • β = regularization parameter, β→0 after r→∞
    Introduced in the coordinate transformation t' = t + βφ to make the conformal boundary spacelike; central charges are independent of β.
  • α = period of t; later fixed to 2πηβ
    Arbitrary periodicity of the time coordinate in the unregularized right-moving Fourier modes; cancels in the final central charge.
assumptions (4)
  • domain assumption The BBC potential formula (B.2) is the correct charge integrand for NMG and TMG, including higher-derivative modifications.
    Equation (B.2) is taken from [35,43,51,52] and stated without derivation in the paper; all central charge computations rely on it.
  • domain assumption The near-horizon metric (2.3) is the extremal BTZ solution in NMG and TMG with the same parameter identifications as Einstein gravity.
    Used in sections 2 and 3; the NMG coupling enters through λ = Λ - Λ²/4m².
  • ad hoc to paper The regularization prescription of [22] (compute charges on the deformed metric and take r→∞ before β→0) yields the correct algebra for the original null-boundary geometry.
    This is the load-bearing methodological premise, discussed below Eq. (2.24); section 4 provides only a consistency check for spacelike boundaries.
  • standard math Central charges are extracted from the p³ coefficient of the central extension term, with subleading p terms handled by a constant shift of L₀.
    Used to convert (2.10) to the standard Virasoro algebra (2.11); the explicit shift is not shown.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Extended Near Horizon Symmetries of Extremal BTZ Black Holes in 3D Massive Gravity." pith.science (2026). https://pith.science/paper/EHZW3AAQ

@misc{pith2026241218286,
  author       = {Pith},
  title        = {Pith review of: Extended Near Horizon Symmetries of Extremal BTZ Black Holes in 3D Massive Gravity},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/EHZW3AAQ}},
  note         = {Machine review of arXiv:2412.18286}
}
read the original abstract

We study the asymptotic symmetries of near-horizon extremal BTZ black holes in higher derivative theories of gravity, such as New Massive Gravity and Topological Massive Gravity. By employing a particular boundary condition and the regularization prescription proposed earlier for the Einstein gravity, we demonstrate the existence of two centrally extended Virasoro algebras. The central charges evaluated within this framework are in agreement with their corresponding expressions evaluated at the spatial infinity. We also discuss the robustness of the regularization procedure by relating asymptotic and near-horizon geometries.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

68 extracted references · 28 canonical work pages

  1. [22]

    On Non-Chiral Extension of Kerr/CFT,

    T. Azeyanagi, N. Ogawa and S. Terashima, “On Non-Chiral Extension of Kerr/CFT,” JHEP 1106, 081 (2011) [arXiv:1102.3423 [hep-th]]

    arXiv 2011

  2. [1]

    Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity,

    J. D. Brown and M. Henneaux, “Central Charges in the Canonical Realization of Asymptotic Symmetries: An Example from Three-Dimensional Gravity,” Commun. Math. Phys.104, 207 (1986)

    work page 1986

  3. [2]

    The Black hole in three-dimensional space-time,

    M. Banados, C. Teitelboim and J. Zanelli, “The Black hole in three-dimensional space-time,” Phys. Rev. Lett.69, 1849-1851 (1992) [arXiv:hep-th/9204099 [hep-th]]

    arXiv 1992

  4. [3]

    Black hole entropy from near-horizon microstates,

    A. Strominger, “Black hole entropy from near-horizon microstates,” JHEP9802 009 (1998), [arXiv:hep-th/9712251]

    arXiv 1998

  5. [4]

    The Kerr/CFT Correspondence,

    M. Guica, T. Hartman, W. Song and A. Strominger, “The Kerr/CFT Correspondence,” Phys. Rev. D 80, 124008 (2009) [arXiv:0809.4266 [hep-th]]

    arXiv 2009

  6. [5]

    The Extreme Kerr throat geometry: A Vacuum analog of AdS(2) x S**2,

    J. M. Bardeen and G. T. Horowitz, “The Extreme Kerr throat geometry: A Vacuum analog of AdS(2) x S**2,” Phys. Rev. D60, 104030 (1999) [arXiv:hep-th/9905099 [hep-th]]

    arXiv 1999

  7. [6]

    Kerr/CFT Correspondence in Diverse Dimensions,

    H. Lu, J. Mei and C. N. Pope, “Kerr/CFT Correspondence in Diverse Dimensions,” JHEP04, 054 (2009) [arXiv:0811.2225 [hep-th]]

    arXiv 2009

  8. [7]

    Holographic Duals of Kaluza-Klein Black Holes

    T. Azeyanagi, N. Ogawa and S. Terashima, “Holographic Duals of Kaluza-Klein Black Holes,” JHEP 04, 061 (2009) [arXiv:0811.4177 [hep-th]]

    work page Pith review arXiv 2009

Show all 68 references
  1. [8]

    Kerr/CFT correspondence and five-dimensional BMPV black holes,

    H. Isono, T. S. Tai and W. Y. Wen, “Kerr/CFT correspondence and five-dimensional BMPV black holes,” Int. J. Mod. Phys. A24, 5659 (2009) [arXiv:0812.4440 [hep-th]]

    2009 arXiv

  2. [9]

    Central Charges in Extreme Black Hole/CFT Correspondence,

    G. Compere, K. Murata and T. Nishioka, “Central Charges in Extreme Black Hole/CFT Correspondence,” JHEP 0905, 077 (2009) [arXiv:0902.1001 [hep-th]]

    2009 arXiv

  3. [10]

    CFT Duals for Extreme Black Holes,

    T. Hartman, K. Murata, T. Nishioka and A. Strominger, “CFT Duals for Extreme Black Holes,” JHEP 0904, 019 (2009) [arXiv:0811.4393 [hep-th]]

    2009 arXiv

  4. [11]

    Extremal Isolated Horizon/CFT Correspondence,

    X. N. Wu and Y. Tian, “Extremal Isolated Horizon/CFT Correspondence,” Phys. Rev. D80, 024014 (2009) [arXiv:0904.1554 [hep-th]]. – 17 –

    2009 arXiv

  5. [12]

    Rasmussen, Int

    J. Rasmussen, Int. J. Mod. Phys. A25, 5517-5527 (2010) doi:10.1142/S0217751X10051001 [arXiv:1004.4773 [hep-th]]

    2010 arXiv

  6. [13]

    Extremal Kerr black hole/CFT correspondence in the five dimensional Gódel universe,

    J. J. Peng and S. Q. Wu, “Extremal Kerr black hole/CFT correspondence in the five dimensional Gódel universe,” Phys. Lett. B673, 216 (2009) [arXiv:0901.0311 [hep-th]]; C. M. Chen and J. E. Wang, “Holographic Duals of Black Holes in Five-dimensional Minimal Supergravity,” Class...

    2009 arXiv

  7. [14]

    Higher-Derivative Corrections to the Asymptotic Virasoro Symmetry of 4d Extremal Black Holes,

    T. Azeyanagi, G. Compere, N. Ogawa, Y. Tachikawa and S. Terashima, “Higher-Derivative Corrections to the Asymptotic Virasoro Symmetry of 4d Extremal Black Holes,” Prog. Theor. Phys. 122, 355 (2009) [arXiv:0903.4176 [hep-th]]

    2009 arXiv

  8. [15]

    Cargese Lectures on the Kerr/CFT Correspondence,

    I. Bredberg, C. Keeler, V. Lysov and A. Strominger, “Cargese Lectures on the Kerr/CFT Correspondence,” Nucl. Phys. B Proc. Suppl.216, 194-210 (2011) [arXiv:1103.2355 [hep-th]]

    2011 arXiv

  9. [16]

    The Kerr/CFT correspondence and its extensions,

    G. Compère, “The Kerr/CFT correspondence and its extensions,” Living Rev. Rel.15, 11 (2012) [arXiv:1203.3561 [hep-th]]

    2012 arXiv

  10. [17]

    The Kerr/CFT Correspondence and String Theory,

    T. Azeyanagi, N. Ogawa and S. Terashima, “The Kerr/CFT Correspondence and String Theory,” Phys. Rev. D79, 106009 (2009) [arXiv:0812.4883 [hep-th]]

    2009 arXiv

  11. [18]

    Near Extremal Kerr Entropy from AdS(2) Quantum Gravity,

    A. Castro and F. Larsen, “Near Extremal Kerr Entropy from AdS(2) Quantum Gravity,” JHEP 12, 037 (2009) [arXiv:0908.1121 [hep-th]]

    2009 arXiv

  12. [19]

    Another Realization of Kerr/CFT Correspondence,

    Y. Matsuo, T. Tsukioka and C. M. Yoo, “Another Realization of Kerr/CFT Correspondence,” Nucl. Phys. B825, 231-241 (2010) [arXiv:0907.0303 [hep-th]]

    2010 arXiv

  13. [20]

    New Near Horizon Limit in Kerr/CFT,

    Y. Matsuo and T. Nishioka, “New Near Horizon Limit in Kerr/CFT,” JHEP12, 073 (2010) [arXiv:1010.4549 [hep-th]]

    2010 arXiv

  14. [21]

    Extremal and nonextremal Kerr/CFT correspondences,

    S. Carlip, “Extremal and nonextremal Kerr/CFT correspondences,” JHEP04, 076 (2011) [arXiv:1101.5136 [gr-qc]]

    2011 arXiv

  15. [23]

    Emergent AdS3 in the Zero Entropy Extremal Black Holes,

    T. Azeyanagi, N. Ogawa and S. Terashima, “Emergent AdS3 in the Zero Entropy Extremal Black Holes,” JHEP03, 004 (2011) [arXiv:1010.4291 [hep-th]]

    2011 arXiv

  16. [24]

    What is a chiral 2d CFT? And what does it have to do with extremal black holes?,

    V. Balasubramanian, J. de Boer, M. M. Sheikh-Jabbari and J. Simon, “What is a chiral 2d CFT? And what does it have to do with extremal black holes?,” JHEP02, 017 (2010) [arXiv:0906.3272 [hep-th]]

    2010 arXiv

  17. [25]

    Near Horizon Limits of Massless BTZ and Their CFT Duals,

    J. de Boer, M. M. Sheikh-Jabbari and J. Simon, “Near Horizon Limits of Massless BTZ and Their CFT Duals,” Class. Quant. Grav.28, 175012 (2011) [arXiv:1011.1897 [hep-th]]

    2011 arXiv

  18. [26]

    Three-Dimensional Massive Gauge Theories,

    S. Deser, R. Jackiw and S. Templeton, “Three-Dimensional Massive Gauge Theories,” Phys. Rev. Lett. 48, 975-978 (1982) S. Deser, R. Jackiw and S. Templeton, “Topologically Massive Gauge Theories,” Annals Phys.140, 372-411 (1982) [erratum: Annals Phys.185, 406 (1988)]

    1982

  19. [27]

    Particle - like solutions to topologically massive gravity,

    G. Clement, “Particle - like solutions to topologically massive gravity,” Class. Quant. Grav.11, L115-L120 (1994) [arXiv:gr-qc/9404004 [gr-qc]]; M. Gürses, “Perfect fluid sources in 2+1 dimensions,” Class. Quant. Grav.11, 2585 (1994); K. A. Moussa, G. Clement and C. Leygnac, “...

    1994 arXiv

  20. [28]

    Black hole mass and angular momentum in topologically massive gravity,

    A. Bouchareb and G. Clement, “Black hole mass and angular momentum in topologically massive gravity,” Class. Quant. Grav.24, 5581-5594 (2007) [arXiv:0706.0263 [gr-qc]]

    2007 arXiv

  21. [29]

    Massive Gravity in Three Dimensions,

    E. A. Bergshoeff, O. Hohm and P. K. Townsend, “Massive Gravity in Three Dimensions,” Phys. Rev. Lett. 102, 201301 (2009) [arXiv:0901.1766 [hep-th]]

    2009 arXiv

  22. [30]

    More on Massive 3D Gravity,

    E. A. Bergshoeff, O. Hohm and P. K. Townsend, “More on Massive 3D Gravity,” Phys. Rev. D 79, 124042 (2009) [arXiv:0905.1259 [hep-th]]

    2009 arXiv

  23. [31]

    Warped AdS(3) black holes in new massive gravity,

    G. Clement, “Warped AdS(3) black holes in new massive gravity,” Class. Quant. Grav.26, 105015 (2009) [arXiv:0902.4634 [hep-th]]

    2009 arXiv

  24. [32]

    Massive 3D Supergravity,

    R. Andringa, E. A. Bergshoeff, M. de Roo, O. Hohm, E. Sezgin and P. K. Townsend, “Massive 3D Supergravity,” Class. Quant. Grav.27, 025010 (2010) [arXiv:0907.4658 [hep-th]]. H. Ahmedov and A. N. Aliev, “The General Type N Solution of New Massive Gravity,” Phys. Lett. B 694, 143...

    2010 arXiv

  25. [33]

    Centrally extended symmetry algebra of asymptotically Godel spacetimes,

    G. Compere and S. Detournay, “Centrally extended symmetry algebra of asymptotically Godel spacetimes,” JHEP 03, 098 (2007) [arXiv:hep-th/0701039 [hep-th]]

    2007 arXiv

  26. [34]

    Brown-Henneaux’s Canonical Approach to Topologically Massive Gravity,

    K. Hotta, Y. Hyakutake, T. Kubota and H. Tanida, “Brown-Henneaux’s Canonical Approach to Topologically Massive Gravity,” JHEP07, 066 (2008) [arXiv:0805.2005 [hep-th]]

    2008 arXiv

  27. [35]

    Semi-classical central charge in topologically massive gravity,

    G. Compere and S. Detournay, “Semi-classical central charge in topologically massive gravity,” Class. Quant. Grav.26, 012001 (2009) [erratum: Class. Quant. Grav.26, 139801 (2009)] [arXiv:0808.1911 [hep-th]]

    2009 arXiv

  28. [36]

    Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity,

    J. Oliva, D. Tempo and R. Troncoso, “Three-dimensional black holes, gravitational solitons, kinks and wormholes for BHT massive gravity,” JHEP07, 011 (2009) [arXiv:0905.1545 [hep-th]]

    2009 arXiv

  29. [37]

    Consistent Boundary Conditions for New Massive Gravity in AdS3,

    Y. Liu and Y. W. Sun, “Consistent Boundary Conditions for New Massive Gravity in AdS3,” JHEP 05, 039 (2009) [arXiv:0903.2933 [hep-th]]

    2009 arXiv

  30. [38]

    Warped AdS(3) Black Holes,

    D. Anninos, W. Li, M. Padi, W. Song and A. Strominger, “Warped AdS(3) Black Holes,” JHEP 03, 130 (2009) [arXiv:0807.3040 [hep-th]]. D. Anninos, M. Esole and M. Guica, “Stability of warped AdS(3) vacua of topologically massive gravity,” JHEP10, 083 (2009) [arXiv:0905.2612 [hep-th]]

    2009 arXiv

  31. [39]

    Boundary conditions for spacelike and timelike warped AdS3 spaces in topologically massive gravity,

    G. Compere and S. Detournay, “Boundary conditions for spacelike and timelike warped AdS3 spaces in topologically massive gravity,” JHEP08, 092 (2009) [arXiv:0906.1243 [hep-th]]

    2009 arXiv

  32. [40]

    Conserved quantities and Virasoro algebra in New massive gravity,

    W. Kim, S. Kulkarni and S. H. Yi, “Conserved quantities and Virasoro algebra in New massive gravity,” JHEP 05, 041 (2013) [arXiv:1303.3691 [hep-th]]

    2013 arXiv

  33. [41]

    Near-Horizon Geometry and Warped Conformal Symmetry,

    H. Afshar, S. Detournay, D. Grumiller and B. Oblak, “Near-Horizon Geometry and Warped Conformal Symmetry,” JHEP03, 187 (2016) [arXiv:1512.08233 [hep-th]]

    2016 arXiv

  34. [42]

    Revisiting Conserved Charges in Higher Curvature Gravitational Theories,

    M. Ghodrati, K. Hajian and M. R. Setare, “Revisiting Conserved Charges in Higher Curvature Gravitational Theories,” Eur. Phys. J. C76, no.12, 701 (2016) [arXiv:1606.04353 [hep-th]]

    2016 arXiv

  35. [43]

    Warped AdS3 black holes in higher derivative gravity theories,

    S. Detournay, L. A. Douxchamps, G. S. Ng and C. Zwikel, “Warped AdS3 black holes in higher derivative gravity theories,” JHEP06, 014 (2016) [arXiv:1602.09089 [hep-th]]

    2016 arXiv

  36. [44]

    BTZ Black Holes and Flat Space Cosmologies in Higher Derivative Theories,

    C. Zwikel, “BTZ Black Holes and Flat Space Cosmologies in Higher Derivative Theories,” Class. Quant. Grav.34, no.8, 085003 (2017) [arXiv:1604.02120 [hep-th]]. – 19 –

    2017 arXiv

  37. [45]

    Conserved Charges in Extended Theories of Gravity,

    H. Adami, M. R. Setare, T. C. Sisman and B. Tekin, “Conserved Charges in Extended Theories of Gravity,” [arXiv:1710.07252 [hep-th]]

    arXiv

  38. [46]

    Horizon symmetries and hairy black holes in AdS,

    L. Donnay, G. Giribet and J. Oliva, “Horizon symmetries and hairy black holes in AdS,” JHEP 09, 120 (2020) [arXiv:2007.08422 [hep-th]]

    2020 arXiv

  39. [47]

    A note on Kerr/CFT and Wald entropy discrepancy in high derivative gravities,

    H. S. Liu and H. Lu, “A note on Kerr/CFT and Wald entropy discrepancy in high derivative gravities,” JHEP 07, 213 (2021) [arXiv:2105.02310 [hep-th]]

    2021 arXiv

  40. [48]

    Near horizon gravitational charges,

    H. S. Liu and P. Mao, “Near horizon gravitational charges,” JHEP05, 123 (2022) [arXiv:2201.10308 [hep-th]]

    2022 arXiv

  41. [49]

    Gravitational energy in quadratic curvature gravities,

    S. Deser and B. Tekin, “Gravitational energy in quadratic curvature gravities,” Phys. Rev. Lett. 89, 101101 (2002) [arXiv:hep-th/0205318 [hep-th]]; S. Deser and B. Tekin, “Energy in generic higher curvature gravity theories,” Phys. Rev. D67, 084009 (2003) [arXiv:hep-th/0212292...

    2002 arXiv

  42. [50]

    Some properties of Noether charge and a proposal for dynamical black hole entropy,

    V. Iyer and R. M. Wald, “Some properties of Noether charge and a proposal for dynamical black hole entropy,” Phys. Rev. D50, 846 (1994) [gr-qc/9403028]; R. M. Wald, “Black hole entropy is the Noether charge,” Phys. Rev. D48, 3427 (1993) [gr-qc/9307038]; R. M. Wald, and A. Zopu...

    1994 arXiv

  43. [51]

    Covariant theory of asymptotic symmetries, conservation laws and central charges,

    G. Barnich and F. Brandt, “Covariant theory of asymptotic symmetries, conservation laws and central charges,” Nucl. Phys. B633 3 (2002) [hep-th/0111246]; G. Barnich and G. Compere, “Surface charge algebra in gauge theories and thermodynamic integrability,” J. Math. Phys.49, 04...

    2002 arXiv

  44. [52]

    Advanced Lectures on General Relativity,

    G. Compere and A. Fiorucci, “Advanced Lectures on General Relativity,” Lect. Notes Phys. 952, pp. (2019) [arXiv:1801.07064 [hep-th]]

    2019 arXiv

  45. [53]

    Quasilocal Conserved Charges in a Covariant Theory of Gravity,

    W. Kim, S. Kulkarni and S. H. Yi, “Quasilocal Conserved Charges in a Covariant Theory of Gravity,” Phys. Rev. Lett.111, no. 8, 081101 (2013) Erratum: [Phys. Rev. Lett.112, no. 7, 079902 (2014)] [arXiv:1306.2138 [hep-th]]

    2013 arXiv

  46. [54]

    Quasi-local charges and asymptotic symmetry generators,

    S. Hyun, S. A. Park and S. H. Yi, “Quasi-local charges and asymptotic symmetry generators,” JHEP 1406, 151 (2014) [arXiv:1403.2196 [hep-th]]

    2014 arXiv

  47. [55]

    Central charges from thermodynamics method in 3D gravity,

    D. Mahdavian Yekta and H. Golchin, “Central charges from thermodynamics method in 3D gravity,” Eur. Phys. J. C80, no.5, 473 (2020) [arXiv:2004.00866 [hep-th]]

    2020 arXiv

  48. [56]

    Aspects of Warped AdS3/CFT2 Correspondence,

    B. Chen, J. j. Zhang, J. d. Zhang and D. l. Zhong, “Aspects of Warped AdS3/CFT2 Correspondence,” JHEP 04, 055 (2013) [arXiv:1302.6643 [hep-th]]

    2013 arXiv

  49. [57]

    Mass and Angular momentum of Black Holes in New Massive Gravity,

    S. Nam, J. D. Park and S. H. Yi, “Mass and Angular momentum of Black Holes in New Massive Gravity,” Phys. Rev. D82, 124049 (2010) [arXiv:1009.1962 [hep-th]]

    2010 arXiv

  50. [58]

    Thermodynamics of Black Hole Horizons and Kerr/CFT Correspondence,

    B. Chen, S. x. Liu and J. j. Zhang, “Thermodynamics of Black Hole Horizons and Kerr/CFT Correspondence,” JHEP 11, 017 (2012) [arXiv:1206.2015 [hep-th]]; B. Chen, Z. Xue and J. J. Zhang, “Note on Thermodynamic Method of Black Hole/CFT Correspondence,” JHEP 03, 102 (2013) [arXiv...

    2012 arXiv

  51. [59]

    Quasilocal conserved charges in the presence of a gravitational Chern-Simons term,

    W. Kim, S. Kulkarni and S. H. Yi, “Quasilocal conserved charges in the presence of a gravitational Chern-Simons term,” Phys. Rev. D88, no. 12, 124004 (2013) [arXiv:1310.1739 [hep-th]]

    2013 arXiv

  52. [60]

    New Boundary Conditions for AdS3,

    G. Compère, W. Song and A. Strominger, “New Boundary Conditions for AdS3,” JHEP05, 152 (2013) [arXiv:1303.2662 [hep-th]]. – 20 –

    2013 arXiv

  53. [61]

    Most general AdS3 boundary conditions,

    D. Grumiller and M. Riegler, “Most general AdS3 boundary conditions,” JHEP 1610, 023 (2016) [arXiv:1608.01308 [hep-th]]

    2016 arXiv

  54. [62]

    Boundary conditions for extremal black holes from 2d gravity,

    S. Detournay, T. Smoes and R. Wutte, “Boundary conditions for extremal black holes from 2d gravity,” SciPost Phys.16, no.5, 141 (2024) [arXiv:2312.08353 [hep-th]]

    2024 arXiv

  55. [63]

    Near Horizon Symmetries of the Non-Extremal Black Hole Solutions of Generalized Minimal Massive Gravity,

    M. R. Setare and H. Adami, “Near Horizon Symmetries of the Non-Extremal Black Hole Solutions of Generalized Minimal Massive Gravity,” Phys. Lett. B760, 411-416 (2016) [arXiv:1606.02273 [hep-th]]; M. R. Setare, J. Oliva and S. N. Sajadi, “Hairy black holes in general minimal ma...

    2016 arXiv

  56. [64]

    On the new massive gravity and AdS/CFT,

    A. Sinha, “On the new massive gravity and AdS/CFT,” JHEP06, 061 (2010) [arXiv:1003.0683 [hep-th]]

    2010 arXiv

  57. [65]

    AdS Black Hole Solutions in the Extended New Massive Gravity,

    S. Nam, J. D. Park and S. H. Yi, “AdS Black Hole Solutions in the Extended New Massive Gravity,” JHEP 07, 058 (2010) [arXiv:1005.1619 [hep-th]]

    2010 arXiv

  58. [66]

    Note on WAdS3 black holes in extended BHT gravity,

    D. M. Yekta, “Note on WAdS3 black holes in extended BHT gravity,” EPL148, no.6, 69001 (2024) [arXiv:2411.18062 [hep-th]]

    2024 arXiv

  59. [67]

    The Curious Case of Null Warped Space,

    D. Anninos, G. Compere, S. de Buyl, S. Detournay and M. Guica, “The Curious Case of Null Warped Space,” JHEP11, 119 (2010) [arXiv:1005.4072 [hep-th]]

    2010 arXiv

  60. [68]

    Mathematica package for Surface Charges

    G. Compère, “Mathematica package for Surface Charges” https://ptm.ulb.be/gcompere/package.html – 21 –

Pith tools

Reviewed August 11, 2026 · model on record in the stance chip above.