pith. machine review for the scientific record. sign in

arxiv: 2604.24834 · v1 · submitted 2026-04-27 · ✦ hep-th

Recognition: unknown

Revisiting near-extremal and near-BPS black holes in AdS3 supergravity

Adam Bac , Alejandra Castro , Diksha Jain
Authors on Pith no claims yet

Pith reviewed 2026-05-08 02:24 UTC · model grok-4.3

classification ✦ hep-th
keywords ads3integralpathquantumanalysisaspectsblackfluctuations
0
0 comments X

The pith

In AdS3 supergravity, the gravitational path integral at low temperatures in the near-horizon region is inequivalent to that of the BTZ background, with distinct contributions from bosonic fluctuations, Chern-Simons fields, and spin-3/2 modes leading to a quantum-level disagreement between near-ext

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

Black holes in anti-de Sitter space with three dimensions (AdS3) serve as a useful toy model for studying quantum gravity because they have exact solutions and connections to conformal field theories via holography. The BTZ black hole is a classic example. At very low temperatures, near the extremal limit where the black hole has maximum rotation or charge, quantum effects become important. The authors use the Euclidean path integral, which is a way to compute quantum probabilities by summing over all possible paths or configurations. They look at fluctuations around the background in both the near-horizon area (close to the black hole) and the far-away asymptotic region. They find that the way bosonic fields fluctuate is affected by boundary conditions in AdS3, and the path integral in the near-horizon isn't the same as for BTZ. They also include contributions from Chern-Simons fields, which are like topological terms in the action, and spin-3/2 modes, which are fermionic fields in supergravity. This leads to differences between the near-extremal case and the near-BPS case, where BPS refers to supersymmetric configurations that preserve some supersymmetry. The analysis shows that near and far regions have different dynamics at the quantum level.

Core claim

the gravitational path integral in the near-horizon region is inequivalent to that around BTZ at low temperature... demonstrates a disagreement in the gravitational path integral at the quantum level.

Load-bearing premise

The analysis assumes that the Euclidean path integral can be reliably computed by separating near-horizon and asymptotic regions with appropriate boundary conditions, and that the contributions from Chern-Simons fields and spin-3/2 modes are fully captured without missing higher-order quantum effects or inconsistencies in the supergravity setup.

read the original abstract

Despite the archetypal status of the BTZ background in quantifying quantum aspects of black holes, several features at low temperatures remain imprecise and incomplete. Here, we systematically investigate the behaviour of the Euclidean path integral at low temperatures in the context of AdS3 supergravity, including an analysis of quantum fluctuations in both the near-horizon and asymptotic regions. We clarify and rectify aspects of the bosonic fluctuations, highlighting the role of boundary conditions in AdS3, and show in particular that the gravitational path integral in the near-horizon region is inequivalent to that around BTZ at low temperature. We further account in detail for the contributions of Chern-Simons fields and spin-3/2 modes, thereby refining the disparities between the near-extremal and near-BPS limits at low temperature. Altogether, our analysis sharpens the distinction between near- and far-region dynamics and demonstrates a disagreement in the gravitational path integral at the quantum level.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The manuscript systematically investigates the Euclidean gravitational path integral at low temperatures in AdS3 supergravity for near-extremal and near-BPS black holes. It rectifies aspects of bosonic fluctuations by emphasizing the role of boundary conditions, performs explicit one-loop determinant calculations in the near-horizon and asymptotic regions, accounts for Chern-Simons fields and spin-3/2 modes, and concludes that the near-horizon path integral is inequivalent to the standard BTZ computation at low temperature, thereby demonstrating a quantum-level disagreement between near- and far-region dynamics.

Significance. If the explicit one-loop calculations hold, the work sharpens the distinction between near-horizon and asymptotic contributions in AdS3 quantum gravity, with implications for the validity of BTZ approximations in the low-temperature regime and for holographic duals of near-extremal/near-BPS states. The detailed inclusion of supergravity modes and boundary-condition corrections provides a more precise framework for thermodynamic and entropy computations beyond semiclassical limits.

major comments (1)
  1. [fluctuation analysis and one-loop determinants] The central inequivalence claim rests on the one-loop determinants computed after separating near-horizon and asymptotic regions. The manuscript should explicitly demonstrate (e.g., via a side-by-side comparison of the resulting partition functions or free energies) that the corrected bosonic boundary conditions produce a quantitatively different result from the BTZ case, rather than only stating the inequivalence.
minor comments (3)
  1. [spin-3/2 modes] Clarify the precise fall-off conditions imposed on the spin-3/2 modes and how they differ between the near-horizon and asymptotic patches; a table summarizing the mode spectra would improve readability.
  2. [conclusions] The abstract states that disparities between near-extremal and near-BPS limits are refined, but the main text should include a concise summary paragraph or equation contrasting the two limits after all corrections are applied.
  3. [Chern-Simons and bosonic sectors] Ensure all one-loop determinant expressions are numbered and cross-referenced when discussing their contributions to the path integral.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper relies on standard assumptions in supergravity and quantum field theory in curved space, with no new free parameters or invented entities introduced in the abstract.

axioms (2)
  • domain assumption The Euclidean path integral is a valid approach to compute quantum effects in AdS3 supergravity at low temperatures.
    Invoked throughout the analysis of fluctuations and path integral behavior.
  • domain assumption Boundary conditions in AdS3 can be chosen to separate near-horizon and asymptotic regions appropriately.
    Highlighted as playing a key role in the bosonic fluctuations.

pith-pipeline@v0.9.0 · 5464 in / 1478 out tokens · 83024 ms · 2026-05-08T02:24:05.393128+00:00 · methodology

discussion (0)

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

Reference graph

Works this paper leans on

66 extracted references · 57 canonical work pages · 1 internal anchor

  1. [1]

    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(1992) 1849–1851,arXiv:hep-th/9204099

    work page Pith review arXiv 1992

  2. [2]

    Geometry of the 2+1 Black Hole

    M. Banados, M. Henneaux, C. Teitelboim, and J. Zanelli, “Geometry of the (2+1) black hole,” Phys. Rev.D48(1993) 1506–1525,arXiv:gr-qc/9302012

    work page Pith review arXiv 1993

  3. [3]

    A one-loop test of the near-AdS 2/near-CFT1 correspondence,

    A. M. Charles and F. Larsen, “A one-loop test of the near-AdS 2/near-CFT1 correspondence,” JHEP07no. 07, (2020) 186,arXiv:1908.03575 [hep-th]

    work page arXiv 2020

  4. [4]

    The statistical mechanics of near-extremal black holes,

    L. V. Iliesiu and G. J. Turiaci, “The statistical mechanics of near-extremal black holes,”JHEP 05(2021) 145,arXiv:2003.02860 [hep-th]

    work page arXiv 2021

  5. [5]

    Heydeman, L

    M. Heydeman, L. V. Iliesiu, G. J. Turiaci, and W. Zhao, “The statistical mechanics of near-BPS black holes,”J. Phys. A55no. 1, (2022) 014004,arXiv:2011.01953 [hep-th]. 61

    work page arXiv 2022

  6. [6]

    Revisiting the Logarithmic Corrections to the Black Hole Entropy,

    L. V. Iliesiu, S. Murthy, and G. J. Turiaci, “Revisiting the logarithmic corrections to the black hole entropy,”JHEP07(2025) 058,arXiv:2209.13608 [hep-th]

    work page arXiv 2025

  7. [7]

    New insights on near-extremal black holes,

    G. J. Turiaci, “New insights on near-extremal black holes,”arXiv:2307.10423 [hep-th]

    work page arXiv

  8. [8]

    Kapec, Y

    D. Kapec, Y. T. A. Law, and C. Toldo, “Quasinormal corrections to near-extremal black hole thermodynamics,”JHEP06(2025) 069,arXiv:2409.14928 [hep-th]

    work page arXiv 2025

  9. [9]

    Kolanowski, D

    M. Kolanowski, D. Marolf, I. Rakic, M. Rangamani, and G. J. Turiaci, “Looking at extremal black holes from very far away,”JHEP04(2025) 020,arXiv:2409.16248 [hep-th]

    work page arXiv 2025

  10. [10]

    From BTZ Perturbations to Schwarzian Modes: A Geometrical and Perturbative Analysis

    L. Acito and M. N. Semp´ e, “From BTZ perturbations to Schwarzian modes: A geometrical and perturbative analysis,”arXiv:2511.07111 [hep-th]

    work page internal anchor Pith review Pith/arXiv arXiv

  11. [11]

    A universal Schwarzian sector in two-dimensional conformal field theories,

    A. Ghosh, H. Maxfield, and G. J. Turiaci, “A universal Schwarzian sector in two-dimensional conformal field theories,”JHEP05(2020) 104,arXiv:1912.07654 [hep-th]

    work page arXiv 2020

  12. [12]

    New boundary conditions for AdS 3,

    G. Comp` ere, W. Song, and A. Strominger, “New boundary conditions for AdS 3,”JHEP05 (2013) 152,arXiv:1303.2662 [hep-th]

    work page arXiv 2013

  13. [13]

    Strings and near-extremal black holes in theories with largeN= 4 superconformal symmetry,

    S. Murthy and M. Rangamani, “Strings and near-extremal black holes in theories with large N= 4 superconformal symmetry,”arXiv:2505.14380 [hep-th]

    work page arXiv

  14. [14]

    Strings in AdS 3: one-loop partition function and near-extremal BTZ thermodynamics,

    C. Ferko, S. Murthy, and M. Rangamani, “Strings in AdS 3: one-loop partition function and near-extremal BTZ thermodynamics,”JHEP05(2025) 010,arXiv:2408.14567 [hep-th]

    work page arXiv 2025

  15. [15]

    Supersymmetry and attractors,

    S. Ferrara and R. Kallosh, “Supersymmetry and attractors,”Phys. Rev.D54(1996) 1514–1524,arXiv:hep-th/9602136

    work page arXiv 1996

  16. [16]

    Universality of supersymmetric attractors,

    S. Ferrara and R. Kallosh, “Universality of supersymmetric attractors,”Phys. Rev.D54(1996) 1525–1534,arXiv:hep-th/9603090

    work page arXiv 1996

  17. [17]

    AdS(3)/CFT(2) to AdS(2)/CFT(1),

    R. K. Gupta and A. Sen, “AdS(3)/CFT(2) to AdS(2)/CFT(1),”JHEP04(2009) 034, arXiv:0806.0053 [hep-th]

    work page arXiv 2009

  18. [18]

    Anti-de Sitter fragmen- tation,

    J. M. Maldacena, J. Michelson, and A. Strominger, “Anti-de Sitter fragmentation,”JHEP02 (1999) 011,arXiv:hep-th/9812073

    work page arXiv 1999

  19. [19]

    Models of AdS_2 Backreaction and Holography

    A. Almheiri and J. Polchinski, “Models of AdS 2 backreaction and holography,”JHEP11 (2015) 014,arXiv:1402.6334 [hep-th]

    work page Pith review arXiv 2015

  20. [20]

    Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space

    J. Maldacena, D. Stanford, and Z. Yang, “Conformal symmetry and its breaking in two dimensional nearly anti-de Sitter space,”PTEP2016no. 12, (2016) 12C104, arXiv:1606.01857 [hep-th]

    work page Pith review arXiv 2016

  21. [21]

    The Kerr/CFT Correspondence

    M. Guica, T. Hartman, W. Song, and A. Strominger, “The Kerr/CFT correspondence,”Phys. Rev.D80(2009) 124008,arXiv:0809.4266 [hep-th]

    work page Pith review arXiv 2009

  22. [22]

    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(2010) 017, arXiv:0906.3272 [hep-th]. 62

    work page arXiv 2010

  23. [23]

    On non-chiral extension of Kerr/CFT,

    T. Azeyanagi, N. Ogawa, and S. Terashima, “On non-chiral extension of Kerr/CFT,”JHEP06 (2011) 081,arXiv:1102.3423 [hep-th]

    work page arXiv 2011

  24. [24]

    A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories,

    A. Achucarro and P. K. Townsend, “A Chern-Simons action for three-dimensional anti-de Sitter supergravity theories,”Phys. Lett.B180(1986) 89

    1986

  25. [25]

    Asymptotic dynamics and asymptotic symmetries of three-dimensional extended AdS supergravity,

    M. Henneaux, L. Maoz, and A. Schwimmer, “Asymptotic dynamics and asymptotic symmetries of three-dimensional extended AdS supergravity,”Annals Phys.282(2000) 31–66, arXiv:hep-th/9910013

    work page arXiv 2000

  26. [26]

    Super Weyl anomalies in the AdS/CFT correspondence,

    M. Nishimura and Y. Tanii, “Super Weyl anomalies in the AdS/CFT correspondence,”Int. J. Mod. Phys. A14(1999) 3731–3744,arXiv:hep-th/9904010

    work page arXiv 1999

  27. [27]

    Anti-de Sitter gravity associated with the supergroupSU(1,1|2)×SU(1,1|2),

    J. R. David, “Anti-de Sitter gravity associated with the supergroupSU(1,1|2)×SU(1,1|2),” Mod. Phys. Lett. A14(1999) 1143–1148,arXiv:hep-th/9904068

    work page arXiv 1999

  28. [28]

    Anti-de Sitter/CFT correspondence in three-dimensional supergravity,

    M. Banados, K. Bautier, O. Coussaert, M. Henneaux, and M. Ortiz, “Anti-de Sitter/CFT correspondence in three-dimensional supergravity,”Phys.Rev.D58(1998) 085020, arXiv:hep-th/9805165

    work page arXiv 1998

  29. [29]

    Extremal higher spin black holes,

    M. Ba˜ nados, A. Castro, A. Faraggi, and J. I. Jottar, “Extremal higher spin black holes,” JHEP04(2016) 077,arXiv:1512.00073 [hep-th]

    work page arXiv 2016

  30. [30]

    Supersymmetric space-times in (2+1) AdS supergravity models,

    J. M. Izquierdo and P. K. Townsend, “Supersymmetric space-times in (2+1) AdS supergravity models,”Class. Quant. Grav.12(1995) 895–924,arXiv:gr-qc/9501018

    work page arXiv 1995

  31. [31]

    Lectures on black holes and the AdS(3)/CFT(2) correspondence,

    P. Kraus, “Lectures on black holes and the AdS(3)/CFT(2) correspondence,”Lect. Notes Phys. 755(2008) 193–247,arXiv:hep-th/0609074

    work page arXiv 2008

  32. [32]

    Partition functions and elliptic genera from supergravity,

    P. Kraus and F. Larsen, “Partition functions and elliptic genera from supergravity,”JHEP01 (2007) 002,arXiv:hep-th/0607138

    work page arXiv 2007

  33. [33]

    Microscopic entropy of AdS 3 black holes revisited,

    F. Larsen and S. Lee, “Microscopic entropy of AdS 3 black holes revisited,”JHEP07(2021) 038,arXiv:2101.08497 [hep-th]

    work page arXiv 2021

  34. [34]

    Supersymmetry of the (2+1) black holes,

    O. Coussaert and M. Henneaux, “Supersymmetry of the (2+1) black holes,”Phys. Rev. Lett. 72(1994) 183–186,arXiv:hep-th/9310194

    work page arXiv 1994

  35. [35]

    Supersymmetric conical defects: Towards a string theoretic description of black hole formation,

    V. Balasubramanian, J. de Boer, E. Keski-Vakkuri, and S. F. Ross, “Supersymmetric conical defects: Towards a string theoretic description of black hole formation,”Phys. Rev. D64no. 6, (2001) 064011,arXiv:hep-th/0011217

    work page arXiv 2001

  36. [36]

    Quantizing gravitational instantons,

    G. W. Gibbons and M. J. Perry, “Quantizing gravitational instantons,”Nuclear Physics B146 no. 1, (1978) 90–108

    1978

  37. [37]

    Quantizing gravity with a cosmological constant,

    S. M. Christensen and M. J. Duff, “Quantizing gravity with a cosmological constant,”Nucl. Phys. B170(1980) 480–506

    1980

  38. [38]

    One-loop Partition Functions of 3D Gravity

    S. Giombi, A. Maloney, and X. Yin, “One-loop partition functions of 3D gravity,”JHEP08 (2008) 007,arXiv:0804.1773 [hep-th]. 63

    work page Pith review arXiv 2008

  39. [39]

    The heat kernel on AdS 3 and its applications,

    J. R. David, M. R. Gaberdiel, and R. Gopakumar, “The heat kernel on AdS 3 and its applications,”JHEP04(2010) 125,arXiv:0911.5085 [hep-th]

    work page arXiv 2010

  40. [40]

    Quantum field theory and the Jones polynomial,

    E. Witten, “Quantum field theory and the Jones polynomial,”Commun. Math. Phys.121 (1989) 351

    1989

  41. [41]

    Perturbative expansion of Chern-Simons theory with noncompact gauge group,

    D. Bar-Natan and E. Witten, “Perturbative expansion of Chern-Simons theory with noncompact gauge group,”Commun. Math. Phys.141(1991) 423–440

    1991

  42. [42]

    Nash,Differential Topology and Quantum Field Theory

    C. Nash,Differential Topology and Quantum Field Theory. Academic press, London, 1991

    1991

  43. [43]

    Chern–Simons Theory in a Knotshell,

    D. Grabovsky, “Chern–Simons Theory in a Knotshell,” 2022

    2022

  44. [44]

    Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral,

    M. Porrati and C. Yu, “Kac-Moody and Virasoro characters from the perturbative Chern-Simons path integral,”JHEP05(2019) 083,arXiv:1903.05100 [hep-th]

    work page arXiv 2019

  45. [45]

    The Yang-Mills equations over Riemann surfaces,

    M. F. Atiyah and R. Bott, “The Yang-Mills equations over Riemann surfaces,”Philos. Trans. R. Soc. London. Ser. A308no. 1505, (03, 1983) 523–615

    1983

  46. [46]

    Higher spin AdS 3 supergravity and its dual CFT,

    T. Creutzig, Y. Hikida, and P. B. Ronne, “Higher spin AdS 3 supergravity and its dual CFT,” JHEP02(2012) 109,arXiv:1111.2139 [hep-th]

    work page arXiv 2012

  47. [47]

    Logarithmic corrections to N=2 black hole entropy: An infrared window into the microstates,

    A. Sen, “Logarithmic corrections to N=2 black hole entropy: An infrared window into the microstates,”Gen. Rel. Grav.44no. 5, (2012) 1207–1266,arXiv:1108.3842 [hep-th]

    work page arXiv 2012

  48. [48]

    Revisiting leading quantum corrections to near extremal black hole thermodynamics,

    N. Banerjee and M. Saha, “Revisiting leading quantum corrections to near extremal black hole thermodynamics,”JHEP07(2023) 010,arXiv:2303.12415 [hep-th]

    work page arXiv 2023

  49. [49]

    Lightcone modular bootstrap and Tauberian theory: A Cardy-like formula for near-extremal black holes,

    S. Pal and J. Qiao, “Lightcone modular bootstrap and Tauberian theory: A Cardy-like formula for near-extremal black holes,”Annales Henri Poincare26no. 3, (2025) 787–844, arXiv:2307.02587 [hep-th]

    work page arXiv 2025

  50. [50]

    Near-extremal quantum cross-section for charged fields and superradiance,

    P. Betzios, O. Papadoulaki, and Y. Zhou, “Near-extremal quantum cross-section for charged fields and superradiance,”JHEP11(2025) 114,arXiv:2507.13896 [hep-th]

    work page arXiv 2025

  51. [51]

    Marolf and J

    D. Marolf and J. E. Santos, “The canonical ensemble reloaded: the complex-stability of Euclidean quantum gravity for black holes in a box,”JHEP08(2022) 215, arXiv:2202.11786 [hep-th]

    work page arXiv 2022

  52. [52]

    Stability of saddles and choices of contour in the Euclidean path integral for linearized gravity: dependence on the DeWitt parameter,

    X. Liu, D. Marolf, and J. E. Santos, “Stability of saddles and choices of contour in the Euclidean path integral for linearized gravity: dependence on the DeWitt parameter,”JHEP 05(2024) 087,arXiv:2310.08555 [hep-th]

    work page arXiv 2024

  53. [53]

    Quantum corrections to the path integral of near extremal de Sitter black holes,

    M. J. Blacker, A. Castro, W. Sybesma, and C. Toldo, “Quantum corrections to the path integral of near extremal de Sitter black holes,”JHEP08(2025) 120,arXiv:2503.14623 [hep-th]

    work page arXiv 2025

  54. [54]

    Higher spin quasinormal modes and one-loop determinants in the BTZ black hole,

    S. Datta and J. R. David, “Higher spin quasinormal modes and one-loop determinants in the BTZ black hole,”JHEP03(2012) 079,arXiv:1112.4619 [hep-th]. 64

    work page arXiv 2012

  55. [55]

    Abramowitz and I

    M. Abramowitz and I. A. Stegun,Handbook of Mathematical Functions. Dover Books on Advanced Mathematics. Dover publ, New York, 1972

    1972

  56. [56]

    Camporesi and A

    R. Camporesi and A. Higuchi, “On the eigenfunctions of the Dirac operator on spheres and real hyperbolic spaces,”J. Geom. Phys.20(1996) 1–18,arXiv:gr-qc/9505009

    work page arXiv 1996

  57. [57]

    Tweaking one-loop determinants in AdS$_3$

    A. Castro, C. Keeler, and P. Szepietowski, “Tweaking one-loop determinants in AdS 3,”JHEP 10(2017) 070,arXiv:1707.06245 [hep-th]

    work page Pith review arXiv 2017

  58. [58]

    Lagrangian formulation of irreducible massive fields of arbitrary spin in (2+1)-dimensions,

    I. V. Tyutin and M. A. Vasiliev, “Lagrangian formulation of irreducible massive fields of arbitrary spin in (2+1)-dimensions,”Teor. Mat. Fiz.113N1(1997) 45–57, arXiv:hep-th/9704132

    work page arXiv 1997

  59. [59]

    Grumiller and M

    D. Grumiller and M. Riegler, “Most general AdS 3 boundary conditions,”JHEP10(2016) 023, arXiv:1608.01308 [hep-th]

    work page arXiv 2016

  60. [60]

    Near-extremal limits of warped CFTs,

    A. Aggarwal, A. Castro, S. Detournay, and B. M¨ uhlmann, “Near-extremal limits of warped CFTs,”SciPost Phys.15no. 2, (2023) 056,arXiv:2211.03770 [hep-th]

    work page arXiv 2023

  61. [61]

    Fermionic Localization of the Schwarzian Theory,

    D. Stanford and E. Witten, “Fermionic localization of the Schwarzian theory,”JHEP10(2017) 008,arXiv:1703.04612 [hep-th]

    work page arXiv 2017

  62. [62]

    Kontsevich and G

    M. Kontsevich and G. Segal, “Wick rotation and the positivity of energy in quantum field theory,”Quart. J. Math. Oxford Ser.72no. 1-2, (2021) 673–699,arXiv:2105.10161 [hep-th]

    work page arXiv 2021

  63. [63]

    One-loop corrections to near-extremal Kerr thermodynamics from semiclassical Virasoro blocks,

    P. Arnaudo, G. Bonelli, and A. Tanzini, “One-loop corrections to near-extremal Kerr thermodynamics from semiclassical Virasoro blocks,”Phys. Rev. Lett.134no. 25, (2025) 251401,arXiv:2412.16057 [hep-th]

    work page arXiv 2025

  64. [64]

    Near-extremal dynamics away from the horizon,

    A. Castro, R. Mancilla, and I. Papadimitriou, “Near-extremal dynamics away from the horizon,”JHEP11(2025) 083,arXiv:2507.01126 [hep-th]

    work page arXiv 2025

  65. [65]

    Black hole emission rates and the AdS/CFT correspondence,

    S. Das and A. Dasgupta, “Black hole emission rates and the AdS/CFT correspondence,” JHEP10(1999) 025,arXiv:hep-th/9907116

    work page arXiv 1999

  66. [66]

    Dirac quasinormal modes of Chern-Simons and BTZ black holes with torsion,

    R. Becar, P. A. Gonzalez, and Y. Vasquez, “Dirac quasinormal modes of Chern-Simons and BTZ black holes with torsion,”Phys. Rev. D89no. 2, (2014) 023001,arXiv:1306.5974 [gr-qc]. 65

    work page arXiv 2014