Papers
Topics
Authors
Recent
Detailed Answer
Quick Answer
Concise responses based on abstracts only
Detailed Answer
Well-researched responses based on abstracts and relevant paper content.
Custom Instructions Pro
Preferences or requirements that you'd like Emergent Mind to consider when generating responses
Gemini 2.5 Flash
Gemini 2.5 Flash 88 tok/s
Gemini 2.5 Pro 52 tok/s Pro
GPT-5 Medium 12 tok/s Pro
GPT-5 High 19 tok/s Pro
GPT-4o 110 tok/s Pro
GPT OSS 120B 470 tok/s Pro
Kimi K2 197 tok/s Pro
2000 character limit reached

Cosmological singularities, holographic complexity and entanglement (2404.00761v3)

Published 31 Mar 2024 in hep-th and gr-qc

Abstract: We study holographic volume complexity for various families of holographic cosmologies with Kasner-like singularities, in particular with $AdS$, hyperscaling violating and Lifshitz asymptotics. We find through extensive numerical studies that the complexity surface always bends in the direction away from the singularity and transitions from spacelike near the boundary to lightlike in the interior. As the boundary anchoring time slice approaches the singularity, the transition to lightlike is more rapid, with the spacelike part shrinking. The complexity functional has vanishing contributions from the lightlike region so in the vicinity of the singularity, complexity is vanishingly small, indicating a dual Kasner state of vanishingly low complexity, suggesting an extreme thinning of the effective degrees of freedom dual to the near singularity region. We also develop further previous studies on extremal surfaces for holographic entanglement entropy, and find that in the IR limit they reveal similar behaviour as complexity.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (97)
  1. J. Maldacena and L. Susskind, “Cool horizons for entangled black holes,” Fortsch. Phys. 61, 781-811 (2013) doi:10.1002/prop.201300020 [arXiv:1306.0533 [hep-th]].
  2. L. Susskind, “Computational Complexity and Black Hole Horizons,” Fortsch. Phys. 64, 24-43 (2016) doi:10.1002/prop.201500092 [arXiv:1402.5674 [hep-th]], [arXiv:1403.5695 [hep-th]].
  3. D. Stanford and L. Susskind, “Complexity and Shock Wave Geometries,” Phys. Rev. D 90, no.12, 126007 (2014) doi:10.1103/PhysRevD.90.126007 [arXiv:1406.2678 [hep-th]].
  4. L. Susskind and Y. Zhao, “Switchbacks and the Bridge to Nowhere,” [arXiv:1408.2823 [hep-th]].
  5. D. A. Roberts, D. Stanford and L. Susskind, “Localized shocks,” JHEP 03, 051 (2015) doi:10.1007/JHEP03(2015)051 [arXiv:1409.8180 [hep-th]].
  6. L. Susskind, “Entanglement is not enough,” Fortsch. Phys. 64, 49-71 (2016) doi:10.1002/prop.201500095 [arXiv:1411.0690 [hep-th]].
  7. L. Susskind, “The Typical-State Paradox: Diagnosing Horizons with Complexity,” Fortsch. Phys. 64, 84-91 (2016) doi:10.1002/prop.201500091 [arXiv:1507.02287 [hep-th]].
  8. M. Alishahiha, “Holographic Complexity,” Phys. Rev. D 92, no.12, 126009 (2015) doi:10.1103/PhysRevD.92.126009 [arXiv:1509.06614 [hep-th]].
  9. A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic Complexity Equals Bulk Action?,” Phys. Rev. Lett. 116, no.19, 191301 (2016) doi:10.1103/PhysRevLett.116.191301 [arXiv:1509.07876 [hep-th]].
  10. J. L. Barbon and E. Rabinovici, “Holographic complexity and spacetime singularities,” JHEP 01, 084 (2016) doi:10.1007/JHEP01(2016)084 [arXiv:1509.09291 [hep-th]].
  11. A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Complexity, action, and black holes,” Phys. Rev. D 93, no.8, 086006 (2016) doi:10.1103/PhysRevD.93.086006 [arXiv:1512.04993 [hep-th]].
  12. R. Q. Yang, “Strong energy condition and complexity growth bound in holography,” Phys. Rev. D 95, no.8, 086017 (2017) doi:10.1103/PhysRevD.95.086017 [arXiv:1610.05090 [gr-qc]].
  13. H. Huang, X. H. Feng and H. Lu, “Holographic Complexity and Two Identities of Action Growth,” Phys. Lett. B 769, 357-361 (2017) doi:10.1016/j.physletb.2017.04.011 [arXiv:1611.02321 [hep-th]].
  14. D. Carmi, R. C. Myers and P. Rath, “Comments on Holographic Complexity,” JHEP 03, 118 (2017) doi:10.1007/JHEP03(2017)118 [arXiv:1612.00433 [hep-th]].
  15. A. Reynolds and S. F. Ross, “Divergences in Holographic Complexity,” Class. Quant. Grav. 34, no.10, 105004 (2017) doi:10.1088/1361-6382/aa6925 [arXiv:1612.05439 [hep-th]].
  16. P. Caputa, N. Kundu, M. Miyaji, T. Takayanagi and K. Watanabe, “Anti-de Sitter Space from Optimization of Path Integrals in Conformal Field Theories,” Phys. Rev. Lett. 119, no.7, 071602 (2017) doi:10.1103/PhysRevLett.119.071602 [arXiv:1703.00456 [hep-th]].
  17. S. Chapman, M. P. Heller, H. Marrochio and F. Pastawski, “Toward a Definition of Complexity for Quantum Field Theory States,” Phys. Rev. Lett. 120, no.12, 121602 (2018) doi:10.1103/PhysRevLett.120.121602 [arXiv:1707.08582 [hep-th]].
  18. D. Carmi, S. Chapman, H. Marrochio, R. C. Myers and S. Sugishita, “On the Time Dependence of Holographic Complexity,” JHEP 11, 188 (2017) doi:10.1007/JHEP11(2017)188 [arXiv:1709.10184 [hep-th]].
  19. W. Cottrell and M. Montero, “Complexity is simple!,” JHEP 02, 039 (2018) doi:10.1007/JHEP02(2018)039 [arXiv:1710.01175 [hep-th]].
  20. J. Couch, S. Eccles, W. Fischler and M. L. Xiao, “Holographic complexity and noncommutative gauge theory,” JHEP 03, 108 (2018) doi:10.1007/JHEP03(2018)108 [arXiv:1710.07833 [hep-th]].
  21. B. Swingle and Y. Wang, “Holographic Complexity of Einstein-Maxwell-Dilaton Gravity,” JHEP 09, 106 (2018) doi:10.1007/JHEP09(2018)106 [arXiv:1712.09826 [hep-th]].
  22. S. Bolognesi, E. Rabinovici and S. R. Roy, “On Some Universal Features of the Holographic Quantum Complexity of Bulk Singularities,” JHEP 06, 016 (2018) doi:10.1007/JHEP06(2018)016 [arXiv:1802.02045 [hep-th]].
  23. M. Alishahiha, A. Faraji Astaneh, M. R. Mohammadi Mozaffar and A. Mollabashi, “Complexity Growth with Lifshitz Scaling and Hyperscaling Violation,” JHEP 07, 042 (2018) doi:10.1007/JHEP07(2018)042 [arXiv:1802.06740 [hep-th]].
  24. C. A. Agón, M. Headrick and B. Swingle, “Subsystem Complexity and Holography,” JHEP 02, 145 (2019) doi:10.1007/JHEP02(2019)145 [arXiv:1804.01561 [hep-th]].
  25. A. Bhattacharyya, P. Caputa, S. R. Das, N. Kundu, M. Miyaji and T. Takayanagi, “Path-Integral Complexity for Perturbed CFTs,” JHEP 07, 086 (2018) doi:10.1007/JHEP07(2018)086 [arXiv:1804.01999 [hep-th]].
  26. S. Chapman, H. Marrochio and R. C. Myers, “Holographic complexity in Vaidya spacetimes. Part I,” JHEP 06, 046 (2018) doi:10.1007/JHEP06(2018)046 [arXiv:1804.07410 [hep-th]].
  27. P. Caputa and J. M. Magan, “Quantum Computation as Gravity,” Phys. Rev. Lett. 122, no.23, 231302 (2019) doi:10.1103/PhysRevLett.122.231302 [arXiv:1807.04422 [hep-th]].
  28. H. A. Camargo, P. Caputa, D. Das, M. P. Heller and R. Jefferson, “Complexity as a novel probe of quantum quenches: universal scalings and purifications,” Phys. Rev. Lett. 122, no.8, 081601 (2019) doi:10.1103/PhysRevLett.122.081601 [arXiv:1807.07075 [hep-th]].
  29. S. Chapman, J. Eisert, L. Hackl, M. P. Heller, R. Jefferson, H. Marrochio and R. C. Myers, “Complexity and entanglement for thermofield double states,” SciPost Phys. 6, no.3, 034 (2019) doi:10.21468/SciPostPhys.6.3.034 [arXiv:1810.05151 [hep-th]].
  30. A. R. Brown, H. Gharibyan, H. W. Lin, L. Susskind, L. Thorlacius and Y. Zhao, “Complexity of Jackiw-Teitelboim gravity,” Phys. Rev. D 99, no.4, 046016 (2019) doi:10.1103/PhysRevD.99.046016 [arXiv:1810.08741 [hep-th]].
  31. A. Belin, A. Lewkowycz and G. Sárosi, “Complexity and the bulk volume, a new York time story,” JHEP 03, 044 (2019) doi:10.1007/JHEP03(2019)044 [arXiv:1811.03097 [hep-th]].
  32. S. Chapman, D. Ge and G. Policastro, “Holographic Complexity for Defects Distinguishes Action from Volume,” JHEP 05, 049 (2019) doi:10.1007/JHEP05(2019)049 [arXiv:1811.12549 [hep-th]].
  33. K. Goto, H. Marrochio, R. C. Myers, L. Queimada and B. Yoshida, “Holographic Complexity Equals Which Action?,” JHEP 02, 160 (2019) doi:10.1007/JHEP02(2019)160 [arXiv:1901.00014 [hep-th]].
  34. A. Bernamonti, F. Galli, J. Hernandez, R. C. Myers, S. M. Ruan and J. Simón, “First Law of Holographic Complexity,” Phys. Rev. Lett. 123, no.8, 081601 (2019) doi:10.1103/PhysRevLett.123.081601 [arXiv:1903.04511 [hep-th]].
  35. T. Ali, A. Bhattacharyya, S. S. Haque, E. H. Kim, N. Moynihan and J. Murugan, “Chaos and Complexity in Quantum Mechanics,” Phys. Rev. D 101, no.2, 026021 (2020) doi:10.1103/PhysRevD.101.026021 [arXiv:1905.13534 [hep-th]].
  36. R. J. Caginalp, “Holographic Complexity in FRW Spacetimes,” Phys. Rev. D 101, no.6, 066027 (2020) doi:10.1103/PhysRevD.101.066027 [arXiv:1906.02227 [hep-th]].
  37. Y. S. An, R. G. Cai, L. Li and Y. Peng, “Holographic complexity growth in an FLRW universe,” Phys. Rev. D 101, no.4, 046006 (2020) doi:10.1103/PhysRevD.101.046006 [arXiv:1909.12172 [hep-th]].
  38. P. Braccia, A. L. Cotrone and E. Tonni, “Complexity in the presence of a boundary,” JHEP 02, 051 (2020) doi:10.1007/JHEP02(2020)051 [arXiv:1910.03489 [hep-th]].
  39. L. Schneiderbauer, W. Sybesma and L. Thorlacius, “Holographic Complexity: Stretching the Horizon of an Evaporating Black Hole,” JHEP 03, 069 (2020) doi:10.1007/JHEP03(2020)069 [arXiv:1911.06800 [hep-th]].
  40. A. Bhattacharyya, S. Das, S. Shajidul Haque and B. Underwood, “Cosmological Complexity,” Phys. Rev. D 101, no.10, 106020 (2020) doi:10.1103/PhysRevD.101.106020 [arXiv:2001.08664 [hep-th]].
  41. R. G. Cai, S. He, S. J. Wang and Y. X. Zhang, “Revisit on holographic complexity in two-dimensional gravity,” JHEP 08, 102 (2020) doi:10.1007/JHEP08(2020)102 [arXiv:2001.11626 [hep-th]].
  42. A. Bhattacharyya, S. Das, S. S. Haque and B. Underwood, “Rise of cosmological complexity: Saturation of growth and chaos,” Phys. Rev. Res. 2, no.3, 033273 (2020) doi:10.1103/PhysRevResearch.2.033273 [arXiv:2005.10854 [hep-th]].
  43. K. X. Zhu, F. W. Shu and D. H. Du, “Holographic complexity for nonlinearly charged Lifshitz black holes,” Class. Quant. Grav. 37, no.19, 195023 (2020) doi:10.1088/1361-6382/aba843 [arXiv:2007.11759 [hep-th]].
  44. A. Bhattacharya, A. Bhattacharyya, P. Nandy and A. K. Patra, “Islands and complexity of eternal black hole and radiation subsystems for a doubly holographic model,” JHEP 05, 135 (2021) doi:10.1007/JHEP05(2021)135 [arXiv:2103.15852 [hep-th]].
  45. S. Jiang and J. Jiang, “Holographic complexity in charged accelerating black holes,” Phys. Lett. B 823, 136731 (2021) doi:10.1016/j.physletb.2021.136731 [arXiv:2106.09371 [hep-th]].
  46. N. Engelhardt and Å. Folkestad, “General bounds on holographic complexity,” JHEP 01, 040 (2022) doi:10.1007/JHEP01(2022)040 [arXiv:2109.06883 [hep-th]].
  47. A. Bhattacharya, A. Bhattacharyya, P. Nandy and A. K. Patra, “Partial islands and subregion complexity in geometric secret-sharing model,” JHEP 12, 091 (2021) doi:10.1007/JHEP12(2021)091 [arXiv:2109.07842 [hep-th]].
  48. S. Chapman, D. A. Galante and E. D. Kramer, “Holographic complexity and de Sitter space,” JHEP 02, 198 (2022) doi:10.1007/JHEP02(2022)198 [arXiv:2110.05522 [hep-th]].
  49. A. Belin, R. C. Myers, S. M. Ruan, G. Sárosi and A. J. Speranza, “Does Complexity Equal Anything?,” Phys. Rev. Lett. 128, no.8, 081602 (2022) doi:10.1103/PhysRevLett.128.081602 [arXiv:2111.02429 [hep-th]].
  50. P. Caputa, D. Das and S. R. Das, “Path integral complexity and Kasner singularities,” JHEP 01, 150 (2022) doi:10.1007/JHEP01(2022)150 [arXiv:2111.04405 [hep-th]].
  51. R. Emparan, A. M. Frassino, M. Sasieta and M. Tomašević, “Holographic complexity of quantum black holes,” JHEP 02, 204 (2022) doi:10.1007/JHEP02(2022)204 [arXiv:2112.04860 [hep-th]].
  52. E. Jørstad, R. C. Myers and S. M. Ruan, “Holographic complexity in dSd+1𝑑1{}_{d+1}start_FLOATSUBSCRIPT italic_d + 1 end_FLOATSUBSCRIPT,” JHEP 05, 119 (2022) doi:10.1007/JHEP05(2022)119 [arXiv:2202.10684 [hep-th]].
  53. Y. S. An, L. Li, F. G. Yang and R. Q. Yang, “Interior structure and complexity growth rate of holographic superconductor from M-theory,” JHEP 08, 133 (2022) doi:10.1007/JHEP08(2022)133 [arXiv:2205.02442 [hep-th]].
  54. T. Mandal, A. Mitra and G. S. Punia, “Action complexity of charged black holes with higher derivative interactions,” Phys. Rev. D 106, no.12, 126017 (2022) doi:10.1103/PhysRevD.106.126017 [arXiv:2205.11201 [hep-th]].
  55. F. Omidi, “Generalized volume-complexity for two-sided hyperscaling violating black branes,” JHEP 01, 105 (2023) doi:10.1007/JHEP01(2023)105 [arXiv:2207.05287 [hep-th]].
  56. S. Chapman, D. A. Galante, E. Harris, S. U. Sheorey and D. Vegh, “Complex geodesics in de Sitter space,” JHEP 03, 006 (2023) doi:10.1007/JHEP03(2023)006 [arXiv:2212.01398 [hep-th]].
  57. R. Auzzi, G. Nardelli, G. P. Ungureanu and N. Zenoni, “Volume complexity of dS bubbles,” Phys. Rev. D 108, no.2, 026006 (2023) doi:10.1103/PhysRevD.108.026006 [arXiv:2302.03584 [hep-th]].
  58. H. Zolfi, “Complexity and Multi-boundary Wormholes in 2 + 1 dimensions,” JHEP 04, 076 (2023) doi:10.1007/JHEP04(2023)076 [arXiv:2302.07522 [hep-th]].
  59. G. Katoch, J. Ren and S. R. Roy, “Quantum complexity and bulk timelike singularities,” JHEP 12, 085 (2023) doi:10.1007/JHEP12(2023)085 [arXiv:2303.02752 [hep-th]].
  60. T. Anegawa, N. Iizuka, S. K. Sake and N. Zenoni, “Is action complexity better for de Sitter space in Jackiw-Teitelboim gravity?,” JHEP 06, 213 (2023) doi:10.1007/JHEP06(2023)213 [arXiv:2303.05025 [hep-th]].
  61. E. Jørstad, R. C. Myers and S. M. Ruan, “Complexity=anything: singularity probes,” JHEP 07, 223 (2023) doi:10.1007/JHEP07(2023)223 [arXiv:2304.05453 [hep-th]].
  62. M. T. Wang, H. Y. Jiang and Y. X. Liu, “Generalized volume-complexity for RN-AdS black hole,” JHEP 07, 178 (2023) doi:10.1007/JHEP07(2023)178 [arXiv:2304.05751 [hep-th]].
  63. A. Bhattacharya, A. Bhattacharyya and A. K. Patra, “Holographic complexity of Jackiw-Teitelboim gravity from Karch-Randall braneworld,” JHEP 07, 060 (2023) doi:10.1007/JHEP07(2023)060 [arXiv:2304.09909 [hep-th]].
  64. T. Anegawa and N. Iizuka, “Shock waves and delay of hyperfast growth in de Sitter complexity,” JHEP 08, 115 (2023) doi:10.1007/JHEP08(2023)115 [arXiv:2304.14620 [hep-th]].
  65. S. Baiguera, R. Berman, S. Chapman and R. C. Myers, “The cosmological switchback effect,” JHEP 07, 162 (2023) doi:10.1007/JHEP07(2023)162 [arXiv:2304.15008 [hep-th]].
  66. S. E. Aguilar-Gutierrez, M. P. Heller and S. Van der Schueren, “Complexity = Anything Can Grow Forever in de Sitter,” [arXiv:2305.11280 [hep-th]].
  67. G. Yadav and H. Rathi, “Yang-Baxter deformed wedge holography,” Phys. Lett. B 852, 138592 (2024) doi:10.1016/j.physletb.2024.138592 [arXiv:2307.01263 [hep-th]].
  68. S. E. Aguilar-Gutierrez, B. Craps, J. Hernandez, M. Khramtsov, M. Knysh and A. Shukla, “Holographic complexity: braneworld gravity versus the Lloyd bound,” [arXiv:2312.12349 [hep-th]].
  69. S. Chapman and G. Policastro, “Quantum computational complexity from quantum information to black holes and back,” Eur. Phys. J. C 82, no.2, 128 (2022) doi:10.1140/epjc/s10052-022-10037-1 [arXiv:2110.14672 [hep-th]].
  70. S. R. Das, J. Michelson, K. Narayan and S. P. Trivedi, “Time dependent cosmologies and their duals,” Phys. Rev. D 74, 026002 (2006) [hep-th/0602107].
  71. S. R. Das, J. Michelson, K. Narayan and S. P. Trivedi, “Cosmologies with Null Singularities and their Gauge Theory Duals,” Phys. Rev. D 75, 026002 (2007) [hep-th/0610053].
  72. A. Awad, S. R. Das, K. Narayan and S. P. Trivedi, “Gauge theory duals of cosmological backgrounds and their energy momentum tensors,” Phys. Rev. D 77, 046008 (2008) [arXiv:0711.2994 [hep-th]].
  73. A. Awad, S. Das, S. Nampuri, K. Narayan, S. Trivedi, “Gauge Theories with Time Dependent Couplings and their Cosmological Duals,” Phys.Rev.D79,046004(2009) [arXiv:0807.1517[hep-th]].
  74. N. Engelhardt, T. Hertog and G. T. Horowitz, “Holographic Signatures of Cosmological Singularities,” Phys. Rev. Lett.  113, 121602 (2014) doi:10.1103/PhysRevLett.113.121602 [arXiv:1404.2309 [hep-th]].
  75. N. Engelhardt, T. Hertog and G. T. Horowitz, “Further Holographic Investigations of Big Bang Singularities,” JHEP 1507, 044 (2015) doi:10.1007/JHEP07(2015)044 [arXiv:1503.08838 [hep-th]].
  76. N. Engelhardt and G. T. Horowitz, “Holographic Consequences of a No Transmission Principle,” Phys. Rev. D 93, no.2, 026005 (2016) doi:10.1103/PhysRevD.93.026005 [arXiv:1509.07509 [hep-th]].
  77. N. Engelhardt and G. T. Horowitz, “New Insights into Quantum Gravity from Gauge/gravity Duality,” Int. J. Mod. Phys. D 25, no.12, 1643002 (2016) doi:10.1142/S0218271816430021 [arXiv:1605.04335 [hep-th]].
  78. B. Craps, “Big Bang Models in String Theory,” Class. Quant. Grav. 23, S849-S881 (2006) doi:10.1088/0264-9381/23/21/S01 [arXiv:hep-th/0605199 [hep-th]].
  79. C. Burgess and L. McAllister, “Challenges for String Cosmology,” Class. Quant. Grav. 28, 204002 (2011) doi:10.1088/0264-9381/28/20/204002 [arXiv:1108.2660 [hep-th]].
  80. A. Manu, K. Narayan and P. Paul, “Cosmological singularities, entanglement and quantum extremal surfaces,” JHEP 04, 200 (2021) doi:10.1007/JHEP04(2021)200 [arXiv:2012.07351 [hep-th]].
  81. K. Goswami, K. Narayan and H. K. Saini, “Cosmologies, singularities and quantum extremal surfaces,” JHEP 03, 201 (2022) doi:10.1007/JHEP03(2022)201 [arXiv:2111.14906 [hep-th]].
  82. T. Hartman and J. Maldacena, “Time Evolution of Entanglement Entropy from Black Hole Interiors,” JHEP 05, 014 (2013) doi:10.1007/JHEP05(2013)014 [arXiv:1303.1080 [hep-th]].
  83. S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT,” Phys. Rev. Lett.  96, 181602 (2006) [hep-th/0603001].
  84. S. Ryu and T. Takayanagi, “Aspects of Holographic Entanglement Entropy,” JHEP 0608, 045 (2006) [hep-th/0605073].
  85. V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal,” JHEP 0707 (2007) 062 [arXiv:0705.0016 [hep-th]].
  86. M. Rangamani and T. Takayanagi, “Holographic Entanglement Entropy,” Lect. Notes Phys.  931, pp.1 (2017) [arXiv:1609.01287 [hep-th]].
  87. K. Narayan, “On aspects of two-dimensional dilaton gravity, dimensional reduction, and holography,” Phys. Rev. D 104, no.2, 026007 (2021) doi:10.1103/PhysRevD.104.026007 [arXiv:2010.12955 [hep-th]].
  88. R. Bhattacharya, K. Narayan and P. Paul, “Cosmological singularities and 2-dimensional dilaton gravity,” JHEP 08, 062 (2020) doi:10.1007/JHEP08(2020)062 [arXiv:2006.09470 [hep-th]].
  89. K. S. Kolekar and K. Narayan, “On AdS22{}_{2}start_FLOATSUBSCRIPT 2 end_FLOATSUBSCRIPT holography from redux, renormalization group flows and c-functions,” JHEP 02, 039 (2019) doi:10.1007/JHEP02(2019)039 [arXiv:1810.12528 [hep-th]].
  90. A. Strominger, “Les Houches lectures on black holes,” [arXiv:hep-th/9501071 [hep-th]].
  91. D. Grumiller, W. Kummer and D. V. Vassilevich, “Dilaton gravity in two-dimensions,” Phys. Rept. 369, 327-430 (2002) doi:10.1016/S0370-1573(02)00267-3 [arXiv:hep-th/0204253 [hep-th]].
  92. T. G. Mertens and G. J. Turiaci, “Solvable models of quantum black holes: a review on Jackiw–Teitelboim gravity,” Living Rev. Rel. 26, no.1, 4 (2023) doi:10.1007/s41114-023-00046-1 [arXiv:2210.10846 [hep-th]].
  93. X. Dong, S. Harrison, S. Kachru, G. Torroba and H. Wang, “Aspects of holography for theories with hyperscaling violation,” JHEP 06, 041 (2012) doi:10.1007/JHEP06(2012)041 [arXiv:1201.1905 [hep-th]].
  94. N. Itzhaki, J. M. Maldacena, J. Sonnenschein and S. Yankielowicz, “Supergravity and the large N limit of theories with sixteen supercharges,” Phys. Rev. D 58, 046004 (1998) [hep-th/9802042].
  95. J. L. F. Barbon and C. A. Fuertes, “Holographic entanglement entropy probes (non)locality,” JHEP 0804, 096 (2008) doi:10.1088/1126-6708/2008/04/096 [arXiv:0803.1928 [hep-th]].
  96. L.D. Landau and E.M. Lifshitz, Course of Theoretical Physics, Vol. 2, “Classical Theory of Fields”, (Pergamon, 1987). This has a transparent treatment of the Bianchi classification of 4-dim cosmologies as well as the BKL analysis.
  97. V. Belinskii and I. Khalatnikov, Sov. Phys. JETP 36 (1973) 591.
List To Do Tasks Checklist Streamline Icon: https://streamlinehq.com

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
Ai Generate Text Spark Streamline Icon: https://streamlinehq.com

Paper Prompts

Sign up for free to create and run prompts on this paper using GPT-5.

List Streamline Icon: https://streamlinehq.com Explore 10 Community Prompts
Dice Question Streamline Icon: https://streamlinehq.com

Follow-up Questions

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets