Journal of Holography Applications in Physics
Holographic Complexity and Residual Entropy of a Rotating BTZ Black Hole within Horndeski Gravity
Document Type : Regular article
Author
Departamento de Física, Universidade Federal do Maranhão, São Luís, 65080-805, Brazil
Abstract
This work explores the holographic complexity and residual entropy of a rotating BTZ black hole within the framework of Horndeski gravity. The investigation is motivated by the need to understand the emission of information from black holes, encoded by quantum complexity, which persists even at zero temperature. Traditionally, black holes are considered to cease emitting information upon reaching zero temperature, yet our findings suggest a minimum level of information or minimal entropy. This challenges the classical notion of black hole death. Recent studies in the context of Horndeski gravity and the AdS/BCFT correspondence have identified a nonzero minimal entropy at zero temperature. Our work shows that complexity and entropy provide crucial insights into the information emission from black holes, extending beyond their classical death. These findings significantly affect our understanding of black hole thermodynamics and quantum information theory.
Keywords
Main Subjects
Article PDF
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[52] N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, “The String landscape, black holes and gravity as the weakest force”, JHEP 06, 060 (2007). DOI:10.1088/1126- 6708/2007/06/060
[2] L. Susskind, “Computational Complexity and Black Hole Horizons”, Fortsch. Phys. 64, 24 (2016). DOI:10.1002/prop.201500092
[3] A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Holographic Complexity Equals Bulk Action?”, Phys. Rev. Lett. 116(19), 191301 (2016). DOI: 10.1103/PhysRevLett.116.191301
[4] A. R. Brown, D. A. Roberts, L. Susskind, B. Swingle and Y. Zhao, “Complexity, action, and black holes”, Phys. Rev. D 93(8), 086006 (2016). DOI:10.1103/PhysRevD.93.086006
[5] L. Susskind, “Black Holes and Complexity Classes”, [arXiv:1802.02175 [hep-th]].
[6] A. R. Brown, H. Gharibyan, H. W. Lin, L. Susskind, L. Thorlacius and Y. Zhao, “Complexity of Jackiw-Teitelboim gravity”, Phys. Rev. D 99(4), 046016 (2019). DOI:10.1103/PhysRevD.99.046016.
[7] A. R. Brown and L. Susskind, “Second law of quantum complexity”, Phys. Rev. D 97(8), 086015 (2018). DOI:10.1103/PhysRevD.97.086015
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[9] S. Raju, Lessons from the information paradox, Phys. Rept. 943, 1 (2022). DOI:10.1016/j.physrep.2021.10.001
[10] X. A. Zhang, A. Ricarte, D. W. Pesce, M. D. Johnson, N. Nagar, R. Narayan, V. Ramakrishnan, S. Doeleman and D. C. M. Palumbo, “Accessing a New Population of Supermassive Black Holes with Extensions to the Event Horizon Telescope”, DOI: 10.3847/1538-4357/adbd45
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[16] S. S. Hashemi, G. Jafari and A. Naseh, “First law of holographic complexity”, Phys. Rev. D 102(10), 106008 (2020). DOI:10.1103/PhysRevD.102.106008
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[18] E. Witten, Adv. Theor. Math. Phys. 2, 253 (1998). DOI:10.4310/ATMP.1998.v2.n2.a2
[19] F. F. Santos, E. F. Capossoli and H. Boschi-Filho, “AdS/BCFT correspondence and BTZ black hole thermodynamics within Horndeski gravity”, Phys. Rev. D 104(6), 066014 (2021). DOI:10.1103/PhysRevD.104.066014
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[21] F. F. Santos, M. Bravo-Gaete, O. Sokoliuk and A. Baransky, “AdS/BCFT Correspondence and Horndeski Gravity in the Presence of Gauge Fields: Holographic Paramagnetism/Ferromagnetism Phase Transition”, Fortsch. Phys. 71(12), 2300008 (2023). DOI:10.1002/prop.202300008
[22] F. F. Santos, M. Bravo-Gaete, M. M. Ferreira and R. Casana, “Magnetized AdS/BCFT Correspondence in Horndeski Gravity”, Fortsch. Phys. 72 (2024). DOI: 10.1002/prop.202400088
[23] G. W. Horndeski, “Second-order scalar-tensor field equations in a four-dimensional space”, Int. J. Theor. Phys. 10, 363 (1974). DOI:10.1007/BF01807638
[24] G. W. Horndeski and A. Silvestri, “50 Years of Horndeski Gravity: Past, Present and Future”, Int. J. Theor. Phys. 63(2), 38 (2024). DOI:10.1007/s10773-024-05558-2
[25] C. Charmousis, E. J. Copeland, A. Padilla and P. M. Saffn, “General second order scalar-tensor theory, self tuning, and the Fab Four”, Phys. Rev. Lett. 108, 051101 (2012). DOI:10.1103/PhysRevLett.108.051101
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[27] J. P. Bruneton, M. Rinaldi, A. Kanfon, A. Hees, S. Schlogel and A. Fuzfa, “Fab Four: When John and George play gravitation and cosmology”, Adv. Astron. 2012, 430694 (2012). DOI:10.1155/2012/430694
[28] L. Heisenberg, “A systematic approach to generalisations of General Relativity and their cosmological implications”, Phys. Rept. 796, 1 (2019). DOI:10.1016/j.physrep.2018.11.006
[29] T. Kobayashi, “Horndeski theory and beyond: a review”, Rept. Prog. Phys. 82(8), 086901 (2019). DOI:10.1088/1361-6633/ab2429
[30] F. F. Santos, “Rotating black hole with a probe string in Horndeski Gravity”, Eur. Phys. J. Plus 135(10), 810 (2020). DOI:10.1140/epjp/s13360-020-00805-x
[31] F. F. Santos, O. Sokoliuk and A. Baransky, “Holographic Complexity of Braneworld in Horndeski Gravity”, Fortsch. Phys. 71(2-3), 2200141 (2023). DOI:10.1002/prop.202200141
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[34] M. Banados, M. Henneaux, C. Teitelboim and J. Zanelli, “Geometry of the (2+1) black hole”, Phys. Rev. D 48, 1506 (1993). [erratum: Phys. Rev. D 88, 069902 (2013)] DOI:10.1103/PhysRevD.48.1506.
[35] L. Susskind, “Trouble for remnants”, [arXiv:hep-th/9501106 [hep-th]]
[36] 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
[37] S. E. Aguilar-Gutierrez, S. Baiguera and N. Zenoni, “Holographic complexity of the extended Schwarzschild-de Sitter space”, JHEP 05, 201 (2024). DOI:10.1007/JHEP05(2024)201
[38] Y. T. Zhou and X. M. Kuang, “Quantum fluctuation on the worldsheet of probe string in BTZ black hole”, Fortsch. Phys. 73, (2025). DOI:10.1002/prop.70001
[39] T. Takayanagi, “Holographic Dual of BCFT”, Phys. Rev. Lett. 107, 101602 (2011). DOI:10.1103/PhysRevLett.107.101602
[40] M. Fujita, T. Takayanagi and E. Tonni, “Aspects of AdS/BCFT”, JHEP 1111, 043 (2011). DOI:10.1007/JHEP11(2011)043
[41] M. Fujita, M. Kaminski and A. Karch, “SL(2,Z) Action on AdS/BCFT and Hall Conductivities”, JHEP 1207, 150 (2012). DOI:10.1007/JHEP07(2012)150
[42] D. Melnikov, E. Orazi and P. Sodano, “On the AdS/BCFT Approach to Quantum Hall Systems”, JHEP 1305, 116 (2013). DOI:10.1007/JHEP05(2013)116
[43] J. M. Magán, D. Melnikov and M. R. O. Silva, “Black Holes in AdS/BCFT and Fluid/Gravity Correspondence”, JHEP 1411, 069 (2014). DOI:10.1007/JHEP11(2014)069
[44] M. Bravo-Gaete and M. Hassaine, “Lifshitz black holes with a time-dependent scalar field in a Horndeski theory”, Phys. Rev. D 89, 104028 (2014). DOI:10.1103/PhysRevD.89.104028
[45] F. Long, S. Chen, M. Wang and J. Jing, “Shadow of a disformal Kerr black hole in quadratic degenerate higher-order scalar–tensor theories”, Eur. Phys. J. C 80(12), 1180 (2020). DOI:10.1140/epjc/s10052-020-08744-8
[46] M. Nozaki, T. Takayanagi and T. Ugajin, “Central Charges for BCFTs and Holography”, JHEP 06, 066 (2012). DOI:10.1007/JHEP06(2012)066
[47] A. Banerjee, A. Kundu and R. R. Poojary, “Rotating black holes in AdS spacetime, extremality, and chaos”, Phys. Rev. D 102(10), 106013 (2020). DOI:10.1103/PhysRevD.102.106013
[48] S. M. Hosseini, K. Hristov and A. Zaffaroni, “An extremization principle for the entropy of rotating BPS black holes in AdS5”, JHEP 07, 106 (2017). DOI:10.1007/JHEP07(2017)106
[49] A. Cabo-Bizet, D. Cassani, D. Martelli and S. Murthy, “Microscopic origin of the Bekenstein-Hawking entropy of supersymmetric AdS5 black holes”, JHEP 10, 062 (2019). DOI:10.1007/JHEP10(2019)062
[50] S. Choi, J. Kim, S. Kim and J. Nahmgoong, “Large AdS black holes from QFT”, [arXiv:1810.12067 [hep-th]]
[51] V. E. Hubeny, “Covariant Residual Entropy”, JHEP 09, 156 (2014). DOI:10.1007/JHEP09(2014)156
[52] N. Arkani-Hamed, L. Motl, A. Nicolis and C. Vafa, “The String landscape, black holes and gravity as the weakest force”, JHEP 06, 060 (2007). DOI:10.1088/1126- 6708/2007/06/060
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Volume 5, Issue 3
September 2025Pages 31-49
- Receive Date: 16 April 2025
- Revise Date: 22 May 2025
- Accept Date: 28 May 2025