Journal of Holography Applications in Physics
κ-Entanglement Entropy from Black Hole
Document Type : Regular article
Authors
1 Departamento de Física, Universidade Federal do Maranhão, São Luís, 65080--805, Brazil.
2 Department of Physics, Indian Institute of Technology, Kanpur 208016, India.
Abstract
In this work, we explore the entanglement entropy equipped with the $\kappa$-algebra. This entanglement entropy is computed through the geometric setup as performed by Hartman-Maldacena, which, in their prescription, finds that the entropy grows linearly in time. In our case, we show that the $\kappa$-algebra embedding provides a richer scenario where the third-order corrections in time added from $\kappa$-algebra to entanglement entropy imply that the growth of quantum correlations between subsystems is more intricate than a simple linear increase into the dynamics of black hole thermalization and quantum information flow. In the context of holography, such corrections suggest that the thermalization process is not instantaneous but involves higher-order interactions between subsystems.
Keywords
- Entanglement Entropy
- Black Hole Interior
- $\kappa$-algebra
- $\kappa$-geometry
- black hole thermalization
- quantum information flow
Main Subjects
Article PDF
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[31] H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas and S. Shashi, “Information Transfer with a Gravitating Bath”, SciPost Phys. 10(5), 103 (2021) [arXiv:2012.04671 [hep-th]].
[32] A. Karch and L. Randall, “Locally localized gravity”, JHEP 05, 008 (2001) [arXiv:hepth/0011156 [hep-th]].
[33] O. DeWolfe, D. Z. Freedman and H. Ooguri, “Holography and defect conformal field theories”, Phys. Rev. D 66, 025009 (2002) [arXiv:hep-th/0111135 [hep-th]].
[34] F. F. Santos, B. Pourhassan and E. N. Saridakis, “de Sitter Versus Antide Sitter in Horndeski-Like Gravity”, Fortsch. Phys. 72(3), 2300228 (2024) doi:10.1002/prop.202300228 [arXiv:2305.05794 [hep-th]].
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[36] T. Hartman and J. Maldacena, “Time Evolution of Entanglement Entropy from Black Hole Interiors”, JHEP 05, 014 (2013) [arXiv:1303.1080 [hep-th]].
[37] J. F. de Sousa and D. P. Pires, “Generalized Entropic Quantum Speed Limits”, [arXiv:2501.11049 [quant-ph]].
[38] G. Kaniadakis, “Non-linear kinetics underlying generalized statistics”, Physica A 296, 405 (2001) [arXiv:cond-mat/0103467].
[39] A. M. Scarfone, “On the κ-Deformed Cyclic Functions and the Generalized Fourier Series in the Framework of the kappa-Algebra”, Entropy 17, 2812 (2015).
[40] V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal”, JHEP 07, 062 (2007) doi:10.1088/1126-6708/2007/07/062 [arXiv:0705.0016 [hep-th]].
[41] T. Nishioka, S. Ryu and T. Takayanagi, “Holographic Entanglement Entropy: An Overview”, J. Phys. A 42, 504008 (2009) doi:10.1088/1751-8113/42/50/504008 [arXiv:0905.0932 [hep-th]].
[42] V. E. Hubeny, “Extremal surfaces as bulk probes in AdS/CFT”, JHEP 07, 093 (2012) doi:10.1007/JHEP07(2012)093 [arXiv:1203.1044 [hep-th]].
[43] T. Faulkner, M. Guica, T. Hartman, R. C. Myers and M. Van Raamsdonk, “Gravitation from Entanglement in Holographic CFTs”, JHEP 03, 051 (2014) doi:10.1007/JHEP03(2014)051 [arXiv:1312.7856 [hep-th]].
[44] J. Maldacena, S. H. Shenker and D. Stanford, “A bound on chaos”, JHEP 08, 106 (2016) doi:10.1007/JHEP08(2016)106 [arXiv:1503.01409 [hep-th]].
[2] G. Kaniadakis, P. Quarati and A. M. Scarfone, “Kinetical foundations of nonconventional statistics”, Physica 305, 76 (2002) doi:10.1016/S0378-4371(01)00643-4 [arXiv:cond-mat/0110066 [cond-mat.stat-mech]].
[3] G. Kaniadakis, M. Lissia and A. M. Scarfone, “Deformed logarithms and entropies”, Physica A 340, 41 (2004) doi:10.1016/j.physa.2004.03.075 [arXiv:cond-mat/0402418 [cond-mat]].
[4] G. Kaniadakis, “Relativistic Roots of κ-Entropy”, Entropy 26(5), 406 (2024) doi:10.3390/e26050406 [arXiv:2405.07678 [cond-mat.stat-mech]].
[5] S. Nojiri, S. D. Odintsov and V. Faraoni, “From nonextensive statistics and black hole entropy to the holographic dark universe”, Phys. Rev. D 105(4), 044042 (2022) doi:10.1103/PhysRevD.105.044042 [arXiv:2201.02424 [gr-qc]].
[6] S. Nojiri, S. D. Odintsov and T. Paul, “Early and late universe holographic cosmology from a new generalized entropy”, Phys. Lett. B 831, 137189 (2022) doi:10.1016/j.physletb.2022.137189
[7] S. Nojiri, S. D. Odintsov and T. Paul, “Microscopic interpretation of generalized entropy”, Phys. Lett. B 847, 138321 (2023) doi:10.1016/j.physletb.2023.138321 [arXiv:2311.03848 [gr-qc]].
[8] S. Nojiri and S. D. Odintsov, “Micro-canonical and canonical description for generalised entropy”, Phys. Lett. B 845, 138130 (2023) doi:10.1016/j.physletb.2023.138130 [arXiv:2304.09014 [gr-qc]].
[9] G. G. Luciano, “Kaniadakis entropy in extreme gravitational and cosmological environments: a review on the state-of-the-art and future prospects”, Eur. Phys. J. B 97(6), 80 (2024) doi:10.1140/epjb/s10051-024-00730-3 [arXiv:2406.11373 [astro-ph.CO]].
[10] G. V. Ambrósio, M. S. Andrade, P. R. F. Alves, C. N. Costa, J. A. Neto and R. Thibes, “Exploring modified Kaniadakis entropy: MOND theory and the Bekenstein bound conjecture”, [arXiv:2405.14799 [gr-qc]].
[11] M. Yarahmadi and A. Salehi, “Using the Kaniadakis horizon entropy in the presence of neutrinos to alleviate the Hubble and S8 tensions”, Eur. Phys. J. C 84(4), 443 (2024) doi:10.1140/epjc/s10052-024-12805-7 [arXiv:2501.07860 [astro-ph.CO]].
[12] J. Lehmann, “A Note on and Generalization of ”Exploring Modified Kaniadakis Entropy: MOND Theory and the Bekenstein Bound Conjecture”, [arXiv:2406.02367 [grqc]].
[13] F. F. Santos, B. G. da Costa and I. S. Gomez, “Studies of transport coeffcients in charged AdS4 black holes on κ-deformed space”, doi:10.22128/JHAP.2022.608.1035 [arXiv:2211.13783 [hep-th]].
[14] F. F. Santos and H. Boschi-Filho, “Black branes in asymptotically Lifshitz spacetimes with arbitrary exponents in κ-Horndeski gravity”, Phys. Rev. D 109, no.6, 064035 (2024) doi:10.1103/PhysRevD.109.064035 [arXiv:2005.14154 [hep-th]].
[15] S. Ryu and T. Takayanagi, “Holographic derivation of entanglement entropy from AdS/CFT”, Phys. Rev. Lett. 96, 181602 (2006) [arXiv:hep-th/0603001 [hep-th]].
[16] F. F. Santos, B. Pourhassan, E. N. Saridakis, O. Sokoliuk, A. Baransky and E. O. Kahya, “Holographic boundary conformal field theory within Horndeski gravity”, JHEP 12, 217 (2025) doi:10.1007/JHEP12(2024)217 [arXiv:2410.18781 [hep-th]].
[17] F. F. Dos Santos, “Entanglement entropy in Horndeski gravity”, JHAP 3(1), 1 (2022) [arXiv:2201.02500 [hep-th]].
[18] E. Caceres, R. Mohan and P. H. Nguyen, “On holographic entanglement entropy of Horndeski black holes”, JHEP 10, 145 (2017) doi:10.1007/JHEP10(2017)145 [arXiv:1707.06322 [hep-th]].
[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) [arXiv:2105.03802 [hep-th]].
[20] F. F. Santos, M. Bravo-Gaete, M. M. Ferreira and R. Casana, “Magnetized AdS/BCFT Correspondence in Horndeski Gravity”, Fortsch. Phys. 72(7-8), 2400088 (2024) doi:10.1002/prop.202400088 [arXiv:2310.17092 [hep-th]].
[21] F. F. Santos and H. Boschi-Filho, “Geometric Josephson junction”, [arXiv:2407.10008 [hep-th]].
[22] T. Takayanagi, “Holographic Dual of BCFT”, Phys. Rev. Lett. 107, 101602 (2011), [arXiv:1105.5165 [hep-th]].
[23] M. Fujita, T. Takayanagi and E. Tonni, “Aspects of AdS/BCFT”, JHEP 1111, 043 (2011), [arXiv:1108.5152 [hep-th]].
[24] H. Kanda, M. Sato, Y. k. Suzuki, T. Takayanagi and Z. Wei, “AdS/BCFT with branelocalized scalar field”, JHEP 03, 105 (2023) [arXiv:2302.03895 [hep-th]].
[25] J. M. Maldacena, “The Large N limit of superconformal field theories and supergravity”, Int. J. Theor. Phys. 38, 1113 (1999) [Adv. Theor. Math. Phys. 2, 231 (1998)] [hepth/9711200].
[26] E. Witten, “Anti-de Sitter space and holography”, Adv. Theor. Math. Phys. 2, 253 (1998) [arXiv:hep-th/9802150 [hep-th]].
[27] H. Farahani, J. Maldacena, L. M. Krauss, S. Upadhyay, S. Mamedov, L. G. Wang, J. Zhang, S. E. San, S. Masood and S. S. Wani, et al. “Proceedings of the 3rd International Conference on Holography and its Applications (ICHA3 2024)”, doi:10.22128/jhap.2024.003.0012
[28] H. Geng, S. Lüst, R. K. Mishra and D. Wakeham, “Holographic BCFTs and Communicating Black Holes”, jhep 08, 003 (2021) [arXiv:2104.07039 [hep-th]].
[29] H. Geng, “Replica Wormholes and Entanglement Islands in the Karch-Randall Braneworld”, [arXiv:2405.14872 [hep-th]].
[30] H. Geng, L. Randall and E. Swanson, “BCFT in a black hole background: an analytical holographic model”, JHEP 12, 056 (2022), [arXiv:2209.02074 [hep-th]].
[31] H. Geng, A. Karch, C. Perez-Pardavila, S. Raju, L. Randall, M. Riojas and S. Shashi, “Information Transfer with a Gravitating Bath”, SciPost Phys. 10(5), 103 (2021) [arXiv:2012.04671 [hep-th]].
[32] A. Karch and L. Randall, “Locally localized gravity”, JHEP 05, 008 (2001) [arXiv:hepth/0011156 [hep-th]].
[33] O. DeWolfe, D. Z. Freedman and H. Ooguri, “Holography and defect conformal field theories”, Phys. Rev. D 66, 025009 (2002) [arXiv:hep-th/0111135 [hep-th]].
[34] F. F. Santos, B. Pourhassan and E. N. Saridakis, “de Sitter Versus Antide Sitter in Horndeski-Like Gravity”, Fortsch. Phys. 72(3), 2300228 (2024) doi:10.1002/prop.202300228 [arXiv:2305.05794 [hep-th]].
[35] F. A. Brito and F. F. Santos, “Braneworlds in Horndeski gravity”, Eur. Phys. J. Plus 137(9), 1051 (2022) [arXiv:1810.08196 [hep-th]].
[36] T. Hartman and J. Maldacena, “Time Evolution of Entanglement Entropy from Black Hole Interiors”, JHEP 05, 014 (2013) [arXiv:1303.1080 [hep-th]].
[37] J. F. de Sousa and D. P. Pires, “Generalized Entropic Quantum Speed Limits”, [arXiv:2501.11049 [quant-ph]].
[38] G. Kaniadakis, “Non-linear kinetics underlying generalized statistics”, Physica A 296, 405 (2001) [arXiv:cond-mat/0103467].
[39] A. M. Scarfone, “On the κ-Deformed Cyclic Functions and the Generalized Fourier Series in the Framework of the kappa-Algebra”, Entropy 17, 2812 (2015).
[40] V. E. Hubeny, M. Rangamani and T. Takayanagi, “A Covariant holographic entanglement entropy proposal”, JHEP 07, 062 (2007) doi:10.1088/1126-6708/2007/07/062 [arXiv:0705.0016 [hep-th]].
[41] T. Nishioka, S. Ryu and T. Takayanagi, “Holographic Entanglement Entropy: An Overview”, J. Phys. A 42, 504008 (2009) doi:10.1088/1751-8113/42/50/504008 [arXiv:0905.0932 [hep-th]].
[42] V. E. Hubeny, “Extremal surfaces as bulk probes in AdS/CFT”, JHEP 07, 093 (2012) doi:10.1007/JHEP07(2012)093 [arXiv:1203.1044 [hep-th]].
[43] T. Faulkner, M. Guica, T. Hartman, R. C. Myers and M. Van Raamsdonk, “Gravitation from Entanglement in Holographic CFTs”, JHEP 03, 051 (2014) doi:10.1007/JHEP03(2014)051 [arXiv:1312.7856 [hep-th]].
[44] J. Maldacena, S. H. Shenker and D. Stanford, “A bound on chaos”, JHEP 08, 106 (2016) doi:10.1007/JHEP08(2016)106 [arXiv:1503.01409 [hep-th]].
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Volume 5, Issue 2
June 2025Pages 57-71
- Receive Date: 17 April 2025
- Revise Date: 10 May 2025
- Accept Date: 11 May 2025