Journal of High Energy Physics

, 2019:47 | Cite as

Jackiw-Teitelboim gravity and rotating black holes

  • Upamanyu MoitraEmail author
  • Sunil Kumar Sake
  • Sandip P. Trivedi
  • V. Vishal
Open Access
Regular Article - Theoretical Physics


We show that the free energy at low temperatures for near-extremal black holes is correctly obtained from the Jackiw-Teitelboim (JT) model of gravity. Our arguments apply to all black holes, including rotating ones, whose metric has a near-horizon AdS2 factor and the associated SL (2, ℝ) symmetry. We verify these arguments by explicit calculations for rotating black holes in 4 and 5 dimensions. Our results suggest that the JT model could prove useful in analysing the dynamics of near-extremal Kerr black holes found in nature.


2D Gravity AdS-CFT Correspondence Black Holes Models of Quantum Gravity 


Open Access

This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited


  1. [1]
    S. Sachdev and J. Ye, Gapless spin fluid ground state in a random, quantum Heisenberg magnet, Phys. Rev. Lett.70 (1993) 3339 [cond-mat/9212030] [INSPIRE].
  2. [2]
    A. Kitaev, A simple model of quantum holography, talks given at KITP, April 7 and May 27 (2015).Google Scholar
  3. [3]
    J. Maldacena, D. Stanford and Z. Yang, Conformal symmetry and its breaking in two dimensional Nearly Anti-de-Sitter space, PTEP2016 (2016) 12C104 [arXiv:1606.01857] [INSPIRE].
  4. [4]
    C. Teitelboim, Gravitation and Hamiltonian structure in two space-time dimensions, Phys. Lett.B 126 (1983) 41.ADSCrossRefGoogle Scholar
  5. [5]
    R. Jackiw, Lower dimensional gravity, Nucl. Phys.B 252 (1985) 343 [INSPIRE].ADSCrossRefGoogle Scholar
  6. [6]
    A. Almheiri and J. Polchinski, Models of AdS 2backreaction and holography, JHEP11 (2015) 014 [arXiv:1402.6334] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  7. [7]
    P. Nayak et al., On the dynamics of near-extremal black holes, JHEP09 (2018) 048 [arXiv:1802.09547] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  8. [8]
    U. Moitra, S.P. Trivedi and V. Vishal, Extremal and near-extremal black holes and near-CFT 1, JHEP07 (2019) 055 [arXiv:1808.08239] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  9. [9]
    T. Muta and S.D. Odintsov, Two-dimensional higher derivative quantum gravity with constant curvature constraint, Prog. Theor. Phys.90 (1993) 247 [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  10. [10]
    J.P.S. Lemos and P.M. Sa, Nonsingular constant curvature two-dimensional black hole, Mod. Phys. Lett.A 9 (1994) 771 [gr-qc/9309023] [INSPIRE].
  11. [11]
    J.P.S. Lemos, Thermodynamics of the two-dimensional black hole in the Teitelboim-Jackiw theory, Phys. Rev.D 54 (1996) 6206 [gr-qc/9608016] [INSPIRE].
  12. [12]
    J. Polchinski and V. Rosenhaus, The spectrum in the Sachdev-Ye-Kitaev model, JHEP04 (2016) 001 [arXiv:1601.06768] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  13. [13]
    A. Jevicki, K. Suzuki and J. Yoon, Bi-local holography in the SYK model, JHEP07 (2016) 007 [arXiv:1603.06246] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  14. [14]
    J. Maldacena and D. Stanford, Remarks on the Sachdev-Ye-Kitaev model, Phys. Rev.D 94 (2016) 106002 [arXiv:1604.07818] [INSPIRE].ADSMathSciNetGoogle Scholar
  15. [15]
    K. Jensen, Chaos in AdS 2holography, Phys. Rev. Lett.117 (2016) 111601 [arXiv:1605.06098] [INSPIRE].ADSCrossRefGoogle Scholar
  16. [16]
    I. Danshita, M. Hanada and M. Tezuka, Creating and probing the Sachdev-Ye-Kitaev model with ultracold gases: Towards experimental studies of quantum gravity, PTEP2017 (2017) 083I01 [arXiv:1606.02454] [INSPIRE].
  17. [17]
    J. Engelsöy, T.G. Mertens and H. Verlinde, An investigation of AdS 2backreaction and holography, JHEP07 (2016) 139 [arXiv:1606.03438] [INSPIRE].ADSzbMATHCrossRefMathSciNetGoogle Scholar
  18. [18]
    A. Almheiri and B. Kang, Conformal symmetry breaking and thermodynamics of near-extremal black holes, JHEP10 (2016) 052 [arXiv:1606.04108] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  19. [19]
    D. Bagrets, A. Altland and A. Kamenev, Sachdev–Ye–Kitaev model as Liouville quantum mechanics, Nucl. Phys.B 911 (2016) 191 [arXiv:1607.00694] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  20. [20]
    M. Cvetič and I. Papadimitriou, AdS 2holographic dictionary, JHEP12 (2016) 008 [Erratum ibid.01 (2017) 120] [arXiv:1608.07018] [INSPIRE].
  21. [21]
    A. Jevicki and K. Suzuki, Bi-local holography in the SYK model: perturbations, JHEP11 (2016) 046 [arXiv:1608.07567] [INSPIRE].MathSciNetzbMATHCrossRefGoogle Scholar
  22. [22]
    Y. Gu, X.-L. Qi and D. Stanford, Local criticality, diffusion and chaos in generalized Sachdev-Ye-Kitaev models, JHEP05 (2017) 125 [arXiv:1609.07832] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  23. [23]
    D.J. Gross and V. Rosenhaus, A generalization of Sachdev-Ye-Kitaev, JHEP02 (2017) 093 [arXiv:1610.01569] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  24. [24]
    M. Berkooz, P. Narayan, M. Rozali and J. Simón, Higher dimensional generalizations of the SYK model, JHEP01 (2017) 138 [arXiv:1610.02422] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  25. [25]
    A.M. García-García and J.J.M. Verbaarschot, Spectral and thermodynamic properties of the Sachdev-Ye-Kitaev model, Phys. Rev.D 94 (2016) 126010 [arXiv:1610.03816] [INSPIRE].ADSGoogle Scholar
  26. [26]
    W. Fu, D. Gaiotto, J. Maldacena and S. Sachdev, Supersymmetric Sachdev-Ye-Kitaev models, Phys. Rev.D 95 (2017) 026009 [arXiv:1610.08917] [INSPIRE].
  27. [27]
    E. Witten, An SYK-like model without disorder, arXiv:1610.09758 [INSPIRE].
  28. [28]
    R. Gurau, The complete 1/N expansion of a SYK–like tensor model, Nucl. Phys.B 916 (2017) 386 [arXiv:1611.04032] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  29. [29]
    J.S. Cotler et al., Black holes and random matrices, JHEP05 (2017) 118 [Erratum ibid.09 (2018) 002] [arXiv:1611.04650] [INSPIRE].
  30. [30]
    I.R. Klebanov and G. Tarnopolsky, Uncolored random tensors, melon diagrams and the Sachdev-Ye-Kitaev models, Phys. Rev.D 95 (2017) 046004 [arXiv:1611.08915] [INSPIRE].
  31. [31]
    R.A. Davison et al., Thermoelectric transport in disordered metals without quasiparticles: The Sachdev-Ye-Kitaev models and holography, Phys. Rev.B 95 (2017) 155131 [arXiv:1612.00849] [INSPIRE].ADSCrossRefGoogle Scholar
  32. [32]
    C. Peng, M. Spradlin and A. Volovich, A supersymmetric SYK-like tensor model, JHEP05 (2017) 062 [arXiv:1612.03851] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  33. [33]
    C. Krishnan, S. Sanyal and P.N. Bala Subramanian, Quantum chaos and holographic tensor models, JHEP03 (2017) 056 [arXiv:1612.06330] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  34. [34]
    G. Turiaci and H. Verlinde, Towards a 2d QFT analog of the SYK model, JHEP10 (2017) 167 [arXiv:1701.00528] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  35. [35]
    T. Li, J. Liu, Y. Xin and Y. Zhou, Supersymmetric SYK model and random matrix theory, JHEP06 (2017) 111 [arXiv:1702.01738] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  36. [36]
    R. Gurau, Quenched equals annealed at leading order in the colored SYK model, EPL119 (2017) 30003 [arXiv:1702.04228] [INSPIRE].ADSCrossRefGoogle Scholar
  37. [37]
    G. Mandal, P. Nayak and S.R. Wadia, Coadjoint orbit action of Virasoro group and two-dimensional quantum gravity dual to SYK/tensor models, JHEP11 (2017) 046 [arXiv:1702.04266] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  38. [38]
    V. Bonzom, L. Lionni and A. Tanasa, Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders, J. Math. Phys.58 (2017) 052301 [arXiv:1702.06944] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  39. [39]
    D.J. Gross and V. Rosenhaus, The bulk dual of SYK: cubic couplings, JHEP05 (2017) 092 [arXiv:1702.08016] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  40. [40]
    D. Stanford and E. Witten, Fermionic localization of the Schwarzian theory, JHEP10 (2017) 008 [arXiv:1703.04612] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  41. [41]
    C. Krishnan, K.V.P. Kumar and S. Sanyal, Random matrices and holographic tensor models, JHEP06 (2017) 036 [arXiv:1703.08155] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  42. [42]
    J. Maldacena, D. Stanford and Z. Yang, Diving into traversable wormholes, Fortsch. Phys.65 (2017) 1700034 [arXiv:1704.05333] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  43. [43]
    S.R. Das, A. Jevicki and K. Suzuki, Three dimensional view of the SYK/AdS duality, JHEP09 (2017) 017 [arXiv:1704.07208] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  44. [44]
    P. Narayan and J. Yoon, SYK-like tensor models on the lattice, JHEP08 (2017) 083 [arXiv:1705.01554] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  45. [45]
    S. Chaudhuri et al., Abelian tensor models on the lattice, Phys. Rev.D 97 (2018) 086007 [arXiv:1705.01930] [INSPIRE].
  46. [46]
    T.G. Mertens, G.J. Turiaci and H.L. Verlinde, Solving the Schwarzian via the conformal bootstrap, JHEP08 (2017) 136 [arXiv:1705.08408] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  47. [47]
    J. Murugan, D. Stanford and E. Witten, More on supersymmetric and 2d analogs of the SYK model, JHEP08 (2017) 146 [arXiv:1706.05362] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  48. [48]
    C. Krishnan and K.V.P. Kumar, Towards a finite-N hologram, JHEP10 (2017) 099 [arXiv:1706.05364] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  49. [49]
    D.J. Gross and V. Rosenhaus, A line of CFTs: from generalized free fields to SYK, JHEP07 (2017) 086 [arXiv:1706.07015] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  50. [50]
    A. Eberlein, V. Kasper, S. Sachdev and J. Steinberg, Quantum quench of the Sachdev-Ye-Kitaev model, Phys. Rev.B 96 (2017) 205123 [arXiv:1706.07803] [INSPIRE].CrossRefGoogle Scholar
  51. [51]
    M. Taylor, Generalized conformal structure, dilaton gravity and SYK, JHEP01 (2018) 010 [arXiv:1706.07812] [INSPIRE].ADSzbMATHGoogle Scholar
  52. [52]
    A.M. García-García, B. Loureiro, A. Romero-Bermúdez and M. Tezuka, Chaotic-integrable transition in the Sachdev-Ye-Kitaev model, Phys. Rev. Lett.120 (2018) 241603 [arXiv:1707.02197] [INSPIRE].
  53. [53]
    I. Kourkoulou and J. Maldacena, Pure states in the SYK model and nearly-AdS 2gravity, arXiv:1707.02325 [INSPIRE].
  54. [54]
    D. Anninos, T. Anous and R.T. D’Agnolo, Marginal deformations & rotating horizons, JHEP12 (2017) 095 [arXiv:1707.03380] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  55. [55]
    S. Giombi, I.R. Klebanov and G. Tarnopolsky, Bosonic tensor models at large N and small 𝜖, Phys. Rev.D 96 (2017) 106014 [arXiv:1707.03866] [INSPIRE].ADSMathSciNetGoogle Scholar
  56. [56]
    J. Sonner and M. Vielma, Eigenstate thermalization in the Sachdev-Ye-Kitaev model, JHEP11 (2017) 149 [arXiv:1707.08013] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  57. [57]
    K. Bulycheva, I.R. Klebanov, A. Milekhin and G. Tarnopolsky, Spectra of operators in large N tensor models, Phys. Rev.D 97 (2018) 026016 [arXiv:1707.09347] [INSPIRE].
  58. [58]
    S. Choudhury et al., Notes on melonic O(N)q−1tensor models, JHEP06 (2018) 094 [arXiv:1707.09352] [INSPIRE].ADSCrossRefGoogle Scholar
  59. [59]
    D. Grumiller et al., Menagerie of AdS 2boundary conditions, JHEP10 (2017) 203 [arXiv:1708.08471] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  60. [60]
    D.J. Gross and V. Rosenhaus, All point correlation functions in SYK, JHEP12 (2017) 148 [arXiv:1710.08113] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  61. [61]
    A. Kitaev and S.J. Suh, The soft mode in the Sachdev-Ye-Kitaev model and its gravity dual, JHEP05 (2018) 183 [arXiv:1711.08467] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  62. [62]
    S.R. Das, A. Ghosh, A. Jevicki and K. Suzuki, Three dimensional view of arbitrary q SYK models, JHEP02 (2018) 162 [arXiv:1711.09839] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  63. [63]
    P. Narayan and J. Yoon, Supersymmetric SYK model with global symmetry, JHEP08 (2018) 159 [arXiv:1712.02647] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  64. [64]
    S.R. Das, A. Ghosh, A. Jevicki and K. Suzuki, Space-time in the SYK model, JHEP07 (2018) 184 [arXiv:1712.02725] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  65. [65]
    H.A. González, D. Grumiller and J. Salzer, Towards a bulk description of higher spin SYK, JHEP05 (2018) 083 [arXiv:1802.01562] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  66. [66]
    C. Krishnan and K.V. Pavan Kumar, Exact solution of a strongly coupled gauge theory in 0 + 1 dimensions, Phys. Rev. Lett.120 (2018) 201603 [arXiv:1802.02502] [INSPIRE].ADSCrossRefGoogle Scholar
  67. [67]
    D.A. Roberts, D. Stanford and A. Streicher, Operator growth in the SYK model, JHEP06 (2018) 122 [arXiv:1802.02633] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  68. [68]
    D. Benedetti and R. Gurau, 2PI effective action for the SYK model and tensor field theories, JHEP05 (2018) 156 [arXiv:1802.05500] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  69. [69]
    A. Gaikwad, L.K. Joshi, G. Mandal and S.R. Wadia, Holographic dual to charged SYK from 3D gravity and Chern-Simons, arXiv:1802.07746 [INSPIRE].
  70. [70]
    I.R. Klebanov, A. Milekhin, F. Popov and G. Tarnopolsky, Spectra of eigenstates in fermionic tensor quantum mechanics, Phys. Rev.D 97 (2018) 106023 [arXiv:1802.10263] [INSPIRE].ADSMathSciNetGoogle Scholar
  71. [71]
    K.S. Kolekar and K. Narayan, AdS 2dilaton gravity from reductions of some nonrelativistic theories, Phys. Rev.D 98 (2018) 046012 [arXiv:1803.06827] [INSPIRE].
  72. [72]
    H. Gharibyan, M. Hanada, S.H. Shenker and M. Tezuka, Onset of random matrix behavior in scrambling systems, JHEP07 (2018) 124 [Erratum ibid.02 (2019) 197] [arXiv:1803.08050] [INSPIRE].
  73. [73]
    J. Maldacena and X.-L. Qi, Eternal traversable wormhole, arXiv:1804.00491 [INSPIRE].
  74. [74]
    D. Harlow and D. Jafferis, The factorization problem in Jackiw-Teitelboim gravity, arXiv:1804.01081 [INSPIRE].
  75. [75]
    A.R. Brown et al., Falling toward charged black holes, Phys. Rev.D 98 (2018) 126016 [arXiv:1804.04156] [INSPIRE].ADSMathSciNetGoogle Scholar
  76. [76]
    H.T. Lam, T.G. Mertens, G.J. Turiaci and H. Verlinde, Shockwave S-matrix from Schwarzian quantum mechanics, JHEP11 (2018) 182 [arXiv:1804.09834] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  77. [77]
    I. Bena, P. Heidmann and D. Turton, AdS 2holography: mind the cap, JHEP12 (2018) 028 [arXiv:1806.02834] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  78. [78]
    P. Saad, S.H. Shenker and D. Stanford, A semiclassical ramp in SYK and in gravity, arXiv:1806.06840 [INSPIRE].
  79. [79]
    S.S. Gubser, C. Jepsen, Z. Ji and B. Trundy, Higher melonic theories, JHEP09 (2018) 049 [arXiv:1806.04800] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  80. [80]
    F. Larsen, A nAttractor mechanism for nAdS 2/nCFT 1holography, JHEP04 (2019) 055 [arXiv:1806.06330] [INSPIRE].ADSCrossRefGoogle Scholar
  81. [81]
    A. Blommaert, T.G. Mertens and H. Verschelde, The Schwarzian theory — A Wilson line perspective, JHEP12 (2018) 022 [arXiv:1806.07765] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  82. [82]
    C.-M. Chang, S. Colin-Ellerin and M. Rangamani, On melonic supertensor models, JHEP10 (2018) 157 [arXiv:1806.09903] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  83. [83]
    G. Gur-Ari, R. Mahajan and A. Vaezi, Does the SYK model have a spin glass phase?, JHEP11 (2018) 070 [arXiv:1806.10145] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  84. [84]
    A. Goel, H.T. Lam, G.J. Turiaci and H. Verlinde, Expanding the black hole interior: partially entangled thermal states in SYK, JHEP02 (2019) 156 [arXiv:1807.03916] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  85. [85]
    J. Lin, Entanglement entropy in Jackiw-Teitelboim gravity, arXiv:1807.06575 [INSPIRE].
  86. [86]
    A. Castro, F. Larsen and I. Papadimitriou, 5D rotating black holes and the nAdS 2/nCFT 1correspondence, JHEP10 (2018) 042 [arXiv:1807.06988] [INSPIRE].ADSCrossRefGoogle Scholar
  87. [87]
    J. Liu, E. Perlmutter, V. Rosenhaus and D. Simmons-Duffin, d-dimensional SYK, AdS Loops and 6j Symbols, JHEP03 (2019) 052 [arXiv:1808.00612] [INSPIRE].
  88. [88]
    S. Giombi et al., Prismatic large N models for bosonic tensors, Phys. Rev.D 98 (2018) 105005 [arXiv:1808.04344] [INSPIRE].ADSMathSciNetGoogle Scholar
  89. [89]
    A. Kitaev and S.J. Suh, Statistical mechanics of a two-dimensional black hole, JHEP05 (2019) 198 [arXiv:1808.07032] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  90. [90]
    K. Pakrouski, I.R. Klebanov, F. Popov and G. Tarnopolsky, Spectrum of Majorana quantum mechanics with O(4)3symmetry, Phys. Rev. Lett.122 (2019) 011601 [arXiv:1808.07455] [INSPIRE].
  91. [91]
    M. Blake, R.A. Davison, S. Grozdanov and H. Liu, Many-body chaos and energy dynamics in holography, JHEP10 (2018) 035 [arXiv:1809.01169] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  92. [92]
    Z. Yang, The quantum gravity dynamics of near extremal black holes, JHEP05 (2019) 205 [arXiv:1809.08647] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  93. [93]
    A.R. Brown et al., Complexity of Jackiw-Teitelboim gravity, Phys. Rev.D 99 (2019) 046016 [arXiv:1810.08741] [INSPIRE].
  94. [94]
    K.S. Kolekar and K. Narayan, On AdS 2holography from redux, renormalization group flows and c-functions, JHEP02 (2019) 039 [arXiv:1810.12528] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  95. [95]
    F. Larsen and Y. Zeng, Black hole spectroscopy and AdS 2holography, JHEP04 (2019) 164 [arXiv:1811.01288] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  96. [96]
    R. Bhattacharya, D.P. Jatkar and N. Sorokhaibam, Quantum quenches and thermalization in SYK models, JHEP07 (2019) 066 [arXiv:1811.06006] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  97. [97]
    M. Alishahiha, On complexity of Jackiw–Teitelboim gravity, Eur. Phys. J.C 79 (2019) 365 [arXiv:1811.09028] [INSPIRE].ADSCrossRefGoogle Scholar
  98. [98]
    A. Dhar et al., Gravitational collapse in SYK models and Choptuik-like phenomenon, arXiv:1812.03979 [INSPIRE].
  99. [99]
    J. Murugan and H. Nastase, One-dimensional bosonization and the SYK model, JHEP08 (2019) 117 [arXiv:1812.11929] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  100. [100]
    K. Goto et al., Holographic complexity equals which action?, JHEP02 (2019) 160 [arXiv:1901.00014] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  101. [101]
    J. Kim, I.R. Klebanov, G. Tarnopolsky and W. Zhao, Symmetry breaking in coupled SYK or tensor models, Phys. Rev.X 9 (2019) 021043 [arXiv:1902.02287] [INSPIRE].
  102. [102]
    S. Sachdev, Universal low temperature theory of charged black holes with AdS 2horizons, J. Math. Phys.60 (2019) 052303 [arXiv:1902.04078] [INSPIRE].
  103. [103]
    A. Blommaert, T.G. Mertens and H. Verschelde, Clocks and rods in Jackiw-Teitelboim quantum gravity, JHEP09 (2019) 060 [arXiv:1902.11194] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  104. [104]
    P. Nayak, J. Sonner and M. Vielma, Eigenstate thermalisation in the conformal Sachdev-Ye-Kitaev model: an analytic approach, JHEP10 (2019) 019 [arXiv:1903.00478] [INSPIRE].ADSCrossRefGoogle Scholar
  105. [105]
    F. Sun, Y. Yi-Xiang, J. Ye and W.M. Liu, Classification of the quantum chaos in colored Sachdev-Ye-Kitaev models, arXiv:1903.02213 [INSPIRE].
  106. [106]
    V. Jahnke, K.-Y. Kim and J. Yoon, On the chaos bound in rotating black holes, JHEP05 (2019) 037 [arXiv:1903.09086] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  107. [107]
    P. Saad, S.H. Shenker and D. Stanford, JT gravity as a matrix integral, arXiv:1903.11115 [INSPIRE].
  108. [108]
    T.G. Mertens, Towards black hole evaporation in Jackiw-Teitelboim gravity, JHEP07 (2019) 097 [arXiv:1903.10485] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  109. [109]
    J. Maldacena, G.J. Turiaci and Z. Yang, Two dimensional nearly de Sitter gravity, arXiv:1904.01911 [INSPIRE].
  110. [110]
    H. Guo, Y. Gu and S. Sachdev, Transport and chaos in lattice Sachdev-Ye-Kitaev models, Phys. Rev.B 100 (2019) 045140 [arXiv:1904.02174] [INSPIRE].
  111. [111]
    T.G. Mertens and G.J. Turiaci, Defects in Jackiw-Teitelboim quantum gravity, JHEP08 (2019) 127 [arXiv:1904.05228] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  112. [112]
    L. Susskind, Complexity and Newton’s laws, arXiv:1904.12819 [INSPIRE].
  113. [113]
    H.W. Lin, J. Maldacena and Y. Zhao, Symmetries near the horizon, JHEP08 (2019) 049 [arXiv:1904.12820] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  114. [114]
    L.V. Iliesiu, S.S. Pufu, H. Verlinde and Y. Wang, An exact quantization of Jackiw-Teitelboim gravity, arXiv:1905.02726 [INSPIRE].
  115. [115]
    J. Cotler, K. Jensen and A. Maloney, Low-dimensional de Sitter quantum gravity, arXiv:1905.03780 [INSPIRE].
  116. [116]
    I.R. Klebanov, P.N. Pallegar and F.K. Popov, Majorana fermion quantum mechanics for higher rank tensors, Phys. Rev.D 100 (2019) 086003 [arXiv:1905.06264] [INSPIRE].
  117. [117]
    F. Sun and J. Ye, Periodic table of SYK and supersymmetric SYK, arXiv:1905.07694 [INSPIRE].
  118. [118]
    V. Rosenhaus, An introduction to the SYK model, arXiv:1807.03334 [INSPIRE].
  119. [119]
    G. Sárosi, AdS 2holography and the SYK model, PoS(Modave2017)001 [arXiv:1711.08482] [INSPIRE].
  120. [120]
    M. Guica, T. Hartman, W. Song and A. Strominger, The Kerr/CFT Correspondence, Phys. Rev.D 80 (2009) 124008 [arXiv:0809.4266] [INSPIRE].ADSMathSciNetGoogle Scholar
  121. [121]
    T. Hartman, K. Murata, T. Nishioka and A. Strominger, CFT duals for extreme black holes, JHEP04 (2009) 019 [arXiv:0811.4393] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  122. [122]
    T. Hartman, W. Song and A. Strominger, Holographic derivation of Kerr-Newman scattering amplitudes for general charge and spin, JHEP03 (2010) 118 [arXiv:0908.3909] [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  123. [123]
    I. Bredberg, T. Hartman, W. Song and A. Strominger, Black hole superradiance from Kerr/CFT, JHEP04 (2010) 019 [arXiv:0907.3477] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  124. [124]
    M. Guica and A. Strominger, Microscopic realization of the Kerr/CFT correspondence, JHEP02 (2011) 010 [arXiv:1009.5039] [INSPIRE].ADSMathSciNetzbMATHGoogle Scholar
  125. [125]
    A. Castro, A. Maloney and A. Strominger, Hidden conformal symmetry of the Kerr black hole, Phys. Rev.D 82 (2010) 024008 [arXiv:1004.0996] [INSPIRE].
  126. [126]
    A.P. Porfyriadis and A. Strominger, Gravity waves from the Kerr/CFT correspondence, Phys. Rev.D 90 (2014) 044038 [arXiv:1401.3746] [INSPIRE].
  127. [127]
    S. Hadar, A.P. Porfyriadis and A. Strominger, Gravity waves from extreme-mass-ratio plunges into Kerr black holes, Phys. Rev.D 90 (2014) 064045 [arXiv:1403.2797] [INSPIRE].
  128. [128]
    S. Hadar, A.P. Porfyriadis and A. Strominger, Fast plunges into Kerr black holes, JHEP07 (2015) 078 [arXiv:1504.07650] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  129. [129]
    A.P. Porfyriadis, Y. Shi and A. Strominger, Photon emission near extreme kerr black holes, Phys. Rev.D 95 (2017) 064009 [arXiv:1607.06028] [INSPIRE].
  130. [130]
    G. Compère, The Kerr/CFT correspondence and its extensions, Living Rev. Rel.15 (2012) 11 [arXiv:1203.3561] [INSPIRE].
  131. [131]
    S.W. Hawking and S.F. Ross, Duality between electric and magnetic black holes, Phys. Rev.D 52 (1995) 5865 [hep-th/9504019] [INSPIRE].ADSMathSciNetGoogle Scholar
  132. [132]
    J.M. Maldacena, J. Michelson and A. Strominger, Anti-de Sitter fragmentation, JHEP02 (1999) 011 [hep-th/9812073] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  133. [133]
    A. Sen, Black hole entropy function and the attractor mechanism in higher derivative gravity, JHEP09 (2005) 038 [hep-th/0506177] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  134. [134]
    A. Sen, Black hole entropy function, attractors and precision counting of microstates, Gen. Rel. Grav.40 (2008) 2249 [arXiv:0708.1270] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  135. [135]
    K. Goldstein, N. Iizuka, R.P. Jena and S.P. Trivedi, Non-supersymmetric attractors, Phys. Rev.D 72 (2005) 124021 [hep-th/0507096] [INSPIRE].ADSGoogle Scholar
  136. [136]
    R.P. Kerr, Gravitational field of a spinning mass as an example of algebraically special metrics, Phys. Rev. Lett.11 (1963) 237 [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  137. [137]
    J.M. Bardeen and G.T. Horowitz, The extreme Kerr throat geometry: a vacuum analog of AdS 2× S 2 , Phys. Rev.D 60 (1999) 104030 [hep-th/9905099] [INSPIRE].ADSMathSciNetGoogle Scholar
  138. [138]
    R.H. Boyer and R.W. Lindquist, Maximal analytic extension of the Kerr metric, J. Math. Phys.8 (1967) 265 [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  139. [139]
    D. Astefanesei et al., Rotating attractors, JHEP10 (2006) 058 [hep-th/0606244] [INSPIRE].ADSMathSciNetCrossRefGoogle Scholar
  140. [140]
    A. Castro and F. Larsen, Near extremal kerr entropy from AdS 2quantum gravity, JHEP12 (2009) 037 [arXiv:0908.1121] [INSPIRE].ADSCrossRefMathSciNetGoogle Scholar
  141. [141]
    S.W. Hawking, C.J. Hunter and M.M. Taylor-Robinson, Rotation and the AdS/CFT correspondence, Phys. Rev.D 59 (1999) 064005 [hep-th/9811056] [INSPIRE].
  142. [142]
    G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, The general Kerr-de Sitter metrics in all dimensions, J. Geom. Phys.53 (2005) 49 [hep-th/0404008] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  143. [143]
    G.W. Gibbons, H. Lü, D.N. Page and C.N. Pope, Rotating black holes in higher dimensions with a cosmological constant, Phys. Rev. Lett.93 (2004) 171102 [hep-th/0409155] [INSPIRE].ADSCrossRefGoogle Scholar
  144. [144]
    S.W. Hawking and H.S. Reall, Charged and rotating AdS black holes and their CFT duals, Phys. Rev.D 61 (2000) 024014 [hep-th/9908109] [INSPIRE].
  145. [145]
    H.K. Kunduri, J. Lucietti and H.S. Reall, Gravitational perturbations of higher dimensional rotating black holes: Tensor perturbations, Phys. Rev.D 74 (2006) 084021 [hep-th/0606076] [INSPIRE].
  146. [146]
    B. Carter, Hamilton-Jacobi and Schrödinger separable solutions of Einstein’s equations, Commun. Math. Phys.10 (1968) 280 [INSPIRE].ADSzbMATHCrossRefGoogle Scholar
  147. [147]
    J.F. Plebański and M. Demiański, Rotating, charged and uniformly accelerating mass in general relativity, Annals Phys.98 (1976) 98 [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  148. [148]
    V. Cardoso, O.J.C. Dias, J.P.S. Lemos and S. Yoshida, The Black hole bomb and superradiant instabilities, Phys. Rev.D 70 (2004) 044039 [Erratum ibid.D 70 (2004) 049903] [hep-th/0404096] [INSPIRE].
  149. [149]
    V. Cardoso and O.J.C. Dias, Small Kerr-anti-de Sitter black holes are unstable, Phys. Rev.D 70 (2004) 084011 [hep-th/0405006] [INSPIRE].
  150. [150]
    V. Cardoso, O.J.C. Dias and S. Yoshida, Classical instability of Kerr-AdS black holes and the issue of final state, Phys. Rev.D 74 (2006) 044008 [hep-th/0607162] [INSPIRE].
  151. [151]
    M.M. Caldarelli, G. Cognola and D. Klemm, Thermodynamics of Kerr-Newman-AdS black holes and conformal field theories, Class. Quant. Grav.17 (2000) 399 [hep-th/9908022] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  152. [152]
    V.A. Kostelecký and M.J. Perry, Solitonic black holes in gauged N = 2 supergravity, Phys. Lett.B 371 (1996) 191 [hep-th/9512222] [INSPIRE].
  153. [153]
    M.M. Caldarelli and D. Klemm, Supersymmetry of Anti-de Sitter black holes, Nucl. Phys.B 545 (1999) 434 [hep-th/9808097] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar
  154. [154]
    J.E. McClintock et al., The spin of the near-extreme kerr black hole GRS 1915+105, Astrophys. J.652 (2006) 518 [astro-ph/0606076] [INSPIRE].
  155. [155]
    J.L. Blum et al., Measuring the spin of GRS 1915+105 with relativistic disk reflection, Astrophys. J.706 (2009) 60 [arXiv:0909.5383] [INSPIRE].ADSCrossRefGoogle Scholar
  156. [156]
    J.M. Miller et al., NuSTAR spectroscopy of GRS 1915+105: disk reflection, spin and connections to jets, Astrophys. J.775 (2013) L45 [arXiv:1308.4669] [INSPIRE].ADSCrossRefGoogle Scholar
  157. [157]
    S. Bhattacharyya, V.E. Hubeny, S. Minwalla and M. Rangamani, Nonlinear Fluid Dynamics from Gravity, JHEP02 (2008) 045 [arXiv:0712.2456] [INSPIRE].ADSCrossRefGoogle Scholar
  158. [158]
    U. Moitra, S.P. Trivedi and V. Vishal, unpublished (2018).Google Scholar
  159. [159]
    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 (2005) 1503 [hep-th/0408217] [INSPIRE].ADSMathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© The Author(s) 2019

Authors and Affiliations

  1. 1.Department of Theoretical PhysicsTata Institute of Fundamental ResearchMumbaiIndia

Personalised recommendations