Abstract
Boltzmann entropy-based thermodynamics of charged anti-de Sitter (AdS) black holes has been shown to exhibit physically interesting features, such as P − V criticalities and van der Waals-like phase transitions. In this work we extend the study of these critical phenomena to Kaniadakis theory, which is a non-extensive generalization of the classical statistical mechanics incorporating relativity. By applying the typical framework of condensed-matter physics, we analyze the impact of Kaniadakis entropy onto the equation of state, the Gibbs free energy and the critical exponents of AdS black holes in the extended phase space. Additionally, we investigate the underlying micro-structure of black holes in Ruppeiner geometry, which reveals appreciable deviations of the nature of the particle interactions from the standard behavior. Our analysis opens up new perspectives on the understanding of black hole thermodynamics in a relativistic statistical framework, highlighting the role of non-extensive corrections in the AdS black holes/van der Waals fluids dual picture.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
S.W. Hawking, Particle Creation by Black Holes, Commun. Math. Phys. 43 (1975) 199 [Erratum ibid. 46 (1976) 206] [INSPIRE].
J.D. Bekenstein, Black holes and entropy, Phys. Rev. D 7 (1973) 2333 [INSPIRE].
J.M. Bardeen, B. Carter and S.W. Hawking, The four laws of black hole mechanics, Commun. Math. Phys. 31 (1973) 161 [INSPIRE].
S.W. Hawking and D.N. Page, Thermodynamics of Black Holes in anti-De Sitter Space, Commun. Math. Phys. 87 (1983) 577 [INSPIRE].
S. Capozziello and M. De Laurentis, Extended Theories of Gravity, Phys. Rept. 509 (2011) 167 [arXiv:1108.6266] [INSPIRE].
R.M. Wald, The thermodynamics of black holes, Living Rev. Rel. 4 (2001) 6 [gr-qc/9912119] [INSPIRE].
F. Weinhold, Metric geometry of equilibrium thermodynamics, J. Chem. Phys. 63 (1975) 2479.
G. Ruppeiner, Thermodynamics: A Riemannian geometric model, Phys. Rev. A 20 (1979) 1608 [INSPIRE].
G. Ruppeiner, Riemannian geometry in thermodynamic fluctuation theory, Rev. Mod. Phys. 67 (1995) 605.
R.-G. Cai and J.-H. Cho, Thermodynamic curvature of the BTZ black hole, Phys. Rev. D 60 (1999) 067502 [hep-th/9803261] [INSPIRE].
S.-W. Wei and Y.-X. Liu, Insight into the Microscopic Structure of an AdS Black Hole from a Thermodynamical Phase Transition, Phys. Rev. Lett. 115 (2015) 111302 [Erratum ibid. 116 (2016) 169903] [arXiv:1502.00386] [INSPIRE].
S.-W. Wei, Y.-X. Liu and R.B. Mann, Repulsive Interactions and Universal Properties of Charged Anti-de Sitter Black Hole Microstructures, Phys. Rev. Lett. 123 (2019) 071103 [arXiv:1906.10840] [INSPIRE].
X.-Y. Guo, H.-F. Li, L.-C. Zhang and R. Zhao, Microstructure and continuous phase transition of a Reissner-Nordström-AdS black hole, Phys. Rev. D 100 (2019) 064036 [arXiv:1901.04703] [INSPIRE].
Z.-M. Xu, B. Wu and W.-L. Yang, Ruppeiner thermodynamic geometry for the Schwarzschild-AdS black hole, Phys. Rev. D 101 (2020) 024018 [arXiv:1910.12182] [INSPIRE].
A. Ghosh and C. Bhamidipati, Thermodynamic geometry and interacting microstructures of BTZ black holes, Phys. Rev. D 101 (2020) 106007 [arXiv:2001.10510] [INSPIRE].
Z.-M. Xu, B. Wu and W.-L. Yang, Diagnosis inspired by the thermodynamic geometry for different thermodynamic schemes of the charged BTZ black hole, Eur. Phys. J. C 80 (2020) 997 [arXiv:2002.00117] [INSPIRE].
E. Hirunsirisawat, R. Nakarachinda and C. Promsiri, Emergent phase, thermodynamic geometry, and criticality of charged black holes from Rényi statistics, Phys. Rev. D 105 (2022) 124049 [arXiv:2204.13023] [INSPIRE].
A. Dehghani, B. Pourhassan, S. Zarepour and E.N. Saridakis, Thermodynamic schemes of charged BTZ-like black holes in arbitrary dimensions, Phys. Dark Univ. 42 (2023) 101371 [arXiv:2305.08219] [INSPIRE].
F.F. Santos, B. Pourhassan and E. Saridakis, de Sitter versus anti-de Sitter in Horndeski-like gravity, arXiv:2305.05794 [INSPIRE].
E. Witten, Anti-de Sitter space and holography, Adv. Theor. Math. Phys. 2 (1998) 253 [hep-th/9802150] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Charged AdS black holes and catastrophic holography, Phys. Rev. D 60 (1999) 064018 [hep-th/9902170] [INSPIRE].
A. Chamblin, R. Emparan, C.V. Johnson and R.C. Myers, Holography, thermodynamics and fluctuations of charged AdS black holes, Phys. Rev. D 60 (1999) 104026 [hep-th/9904197] [INSPIRE].
C. Niu, Y. Tian and X.-N. Wu, Critical Phenomena and Thermodynamic Geometry of RN-AdS Black Holes, Phys. Rev. D 85 (2012) 024017 [arXiv:1104.3066] [INSPIRE].
A. Sahay, T. Sarkar and G. Sengupta, Thermodynamic Geometry and Phase Transitions in Kerr-Newman-AdS Black Holes, JHEP 04 (2010) 118 [arXiv:1002.2538] [INSPIRE].
A. Sahay, T. Sarkar and G. Sengupta, On the Thermodynamic Geometry and Critical Phenomena of AdS Black Holes, JHEP 07 (2010) 082 [arXiv:1004.1625] [INSPIRE].
D. Kubiznak and R.B. Mann, P-V criticality of charged AdS black holes, JHEP 07 (2012) 033 [arXiv:1205.0559] [INSPIRE].
D. Kastor, S. Ray and J. Traschen, Enthalpy and the Mechanics of AdS Black Holes, Class. Quant. Grav. 26 (2009) 195011 [arXiv:0904.2765] [INSPIRE].
B.P. Dolan, The cosmological constant and the black hole equation of state, Class. Quant. Grav. 28 (2011) 125020 [arXiv:1008.5023] [INSPIRE].
B.P. Dolan, Pressure and volume in the first law of black hole thermodynamics, Class. Quant. Grav. 28 (2011) 235017 [arXiv:1106.6260] [INSPIRE].
T.-F. Gong, J. Jiang and M. Zhang, Holographic thermodynamics of rotating black holes, JHEP 06 (2023) 105 [arXiv:2305.00267] [INSPIRE].
M.B. Ahmed et al., Holographic CFT phase transitions and criticality for rotating AdS black holes, JHEP 08 (2023) 142 [arXiv:2305.03161] [INSPIRE].
G. ’t Hooft, Dimensional reduction in quantum gravity, Conf. Proc. C 930308 (1993) 284 [gr-qc/9310026] [INSPIRE].
L. Susskind, The world as a hologram, J. Math. Phys. 36 (1995) 6377 [hep-th/9409089] [INSPIRE].
C. Tsallis and L.J.L. Cirto, Black hole thermodynamical entropy, Eur. Phys. J. C 73 (2013) 2487 [arXiv:1202.2154] [INSPIRE].
H. Quevedo, M.N. Quevedo and A. Sanchez, Quasi-homogeneous black hole thermodynamics, Eur. Phys. J. C 79 (2019) 229 [arXiv:1812.10599] [INSPIRE].
C. Tsallis, Possible Generalization of Boltzmann-Gibbs Statistics, J. Statist. Phys. 52 (1988) 479 [INSPIRE].
J.D. Barrow, The Area of a Rough Black Hole, Phys. Lett. B 808 (2020) 135643 [arXiv:2004.09444] [INSPIRE].
S. Nojiri, S.D. Odintsov and V. Faraoni, From nonextensive statistics and black hole entropy to the holographic dark universe, Phys. Rev. D 105 (2022) 044042 [arXiv:2201.02424] [INSPIRE].
A. Rényi, On the dimension and entropy of probability distributions, Acta Math. Acad. Sci. Hung. 10 (1959) 193.
B.D. Sharma and D.P. Mittal, New non-additive measures of relative information, J. Comb. Inf. Syst. Sci. 2 (1977) 122.
E.N. Saridakis, Barrow holographic dark energy, Phys. Rev. D 102 (2020) 123525 [arXiv:2005.04115] [INSPIRE].
E.N. Saridakis, K. Bamba, R. Myrzakulov and F.K. Anagnostopoulos, Holographic dark energy through Tsallis entropy, JCAP 12 (2018) 012 [arXiv:1806.01301] [INSPIRE].
M. Tavayef, A. Sheykhi, K. Bamba and H. Moradpour, Tsallis Holographic Dark Energy, Phys. Lett. B 781 (2018) 195 [arXiv:1804.02983] [INSPIRE].
G.G. Luciano, Cosmic evolution and thermal stability of Barrow holographic dark energy in a nonflat Friedmann-Robertson-Walker Universe, Phys. Rev. D 106 (2022) 083530 [arXiv:2210.06320] [INSPIRE].
G.G. Luciano, From the emergence of cosmic space to horizon thermodynamics in Barrow entropy-based Cosmology, Phys. Lett. B 838 (2023) 137721 [INSPIRE].
A. Sheykhi and B. Farsi, Growth of perturbations in Tsallis and Barrow cosmology, Eur. Phys. J. C 82 (2022) 1111 [arXiv:2205.04138] [INSPIRE].
H. Shababi and K. Ourabah, Non-Gaussian statistics from the generalized uncertainty principle, Eur. Phys. J. Plus 135 (2020) 697 [INSPIRE].
G.G. Luciano, Tsallis statistics and generalized uncertainty principle, Eur. Phys. J. C 81 (2021) 672 [INSPIRE].
G.G. Luciano and M. Blasone, Nonextensive Tsallis statistics in Unruh effect for Dirac neutrinos, Eur. Phys. J. C 81 (2021) 995 [arXiv:2107.11402] [INSPIRE].
P. Jizba and G. Lambiase, Tsallis cosmology and its applications in dark matter physics with focus on IceCube high-energy neutrino data, Eur. Phys. J. C 82 (2022) 1123 [arXiv:2206.12910] [INSPIRE].
G. Kaniadakis, Non-linear kinetics underlying generalized statistics, Physica A 296 (2001) 405.
G. Kaniadakis, Statistical mechanics in the context of special relativity, Phys. Rev. E 66 (2002) 056125 [cond-mat/0210467] [INSPIRE].
G. Kaniadakis, Statistical mechanics in the context of special relativity. II, Phys. Rev. E 72 (2005) 036108 [cond-mat/0507311] [INSPIRE].
G. Kaniadakis, M. Lissia and A.M. Scarfone, Two-parameter deformations of logarithm, exponential, and entropy: a consistent framework for generalized statistical mechanics, Phys. Rev. E 71 (2005) 046128 [cond-mat/0409683] [INSPIRE].
G. Kaniadakis, P. Quarati and A.M. Scarfone, Kinetical foundations of non-conventional statistics, Physica 305 (2002) 76 [cond-mat/0110066] [INSPIRE].
G.G. Luciano, Gravity and Cosmology in Kaniadakis Statistics: Current Status and Future Challenges, Entropy 24 (2022) 1712 [INSPIRE].
H. Moradpour, A.H. Ziaie and M. Kord Zangeneh, Generalized entropies and corresponding holographic dark energy models, Eur. Phys. J. C 80 (2020) 732 [arXiv:2005.06271] [INSPIRE].
A. Lymperis, S. Basilakos and E.N. Saridakis, Modified cosmology through Kaniadakis horizon entropy, Eur. Phys. J. C 81 (2021) 1037 [arXiv:2108.12366] [INSPIRE].
N. Drepanou, A. Lymperis, E.N. Saridakis and K. Yesmakhanova, Kaniadakis holographic dark energy and cosmology, Eur. Phys. J. C 82 (2022) 449 [arXiv:2109.09181] [INSPIRE].
A. Hernández-Almada et al., Kaniadakis-holographic dark energy: observational constraints and global dynamics, Mon. Not. Roy. Astron. Soc. 511 (2022) 4147 [arXiv:2111.00558] [INSPIRE].
A. Hernández-Almada et al., Observational constraints and dynamical analysis of Kaniadakis horizon-entropy cosmology, Mon. Not. Roy. Astron. Soc. 512 (2022) 5122 [arXiv:2112.04615] [INSPIRE].
G. Lambiase, G.G. Luciano and A. Sheykhi, Slow-roll inflation and growth of perturbations in Kaniadakis modification of Friedmann cosmology, Eur. Phys. J. C 83 (2023) 936 [arXiv:2307.04027] [INSPIRE].
E.M.C. Abreu, J. Ananias Neto, E.M. Barboza and R.C. Nunes, Jeans instability criterion from the viewpoint of Kaniadakis’ statistics, EPL 114 (2016) 55001 [arXiv:1603.00296] [INSPIRE].
I. Cimidiker, M.P. Dabrowski and H. Gohar, Generalized uncertainty principle impact on nonextensive black hole thermodynamics, Class. Quant. Grav. 40 (2023) 145001 [arXiv:2301.00609] [INSPIRE].
A. Kempf, G. Mangano and R.B. Mann, Hilbert space representation of the minimal length uncertainty relation, Phys. Rev. D 52 (1995) 1108 [hep-th/9412167] [INSPIRE].
G.G. Luciano and L. Petruzziello, Generalized uncertainty principle and its implications on geometric phases in quantum mechanics, Eur. Phys. J. Plus 136 (2021) 179 [INSPIRE].
T.S. Biró and V.G. Czinner, A q-parameter bound for particle spectra based on black hole thermodynamics with Rényi entropy, Phys. Lett. B 726 (2013) 861 [arXiv:1309.4261] [INSPIRE].
V.G. Czinner and H. Iguchi, Thermodynamics, stability and Hawking-Page transition of Kerr black holes from Rényi statistics, Eur. Phys. J. C 77 (2017) 892 [arXiv:1702.05341] [INSPIRE].
S. Ghaffari et al., Black hole thermodynamics in Sharma-Mittal generalized entropy formalism, Gen. Rel. Grav. 51 (2019) 93 [arXiv:1901.01506] [INSPIRE].
H. Moradpour, A.H. Ziaie and C. Corda, Tsallis uncertainty, Europhys. Lett. 134 (2021) 20003.
H. Moradpour et al., The third law of thermodynamics, non-extensivity and energy definition in black hole physics, Mod. Phys. Lett. A 37 (2022) 2250076 [arXiv:2106.00378] [INSPIRE].
S. Nojiri, S.D. Odintsov and V. Faraoni, Area-law versus Rényi and Tsallis black hole entropies, Phys. Rev. D 104 (2021) 084030 [arXiv:2109.05315] [INSPIRE].
S. Nojiri, S.D. Odintsov and V. Faraoni, Alternative entropies and consistent black hole thermodynamics, Int. J. Geom. Meth. Mod. Phys. 19 (2022) 2250210 [arXiv:2207.07905] [INSPIRE].
N. Goldenfeld, Lectures on phase transitions and the renormalization group, CRC Press (1992) [https://doi.org/10.1201/9780429493492] [INSPIRE].
H. Reissner, Über die eigengravitation des elektrischen feldes nach der einsteinschen theorie, Annalen Phys. 355 (1916) 106.
E.N. Saridakis, Modified cosmology through spacetime thermodynamics and Barrow horizon entropy, JCAP 07 (2020) 031 [arXiv:2006.01105] [INSPIRE].
S. Rani, A. Jawad, H. Moradpour and A. Tanveer, Tsallis entropy inspires geometric thermodynamics of specific black hole, Eur. Phys. J. C 82 (2022) 713 [INSPIRE].
A. Jawad and S.R. Fatima, Thermodynamic geometries analysis of charged black holes with barrow entropy, Nucl. Phys. B 976 (2022) 115697 [INSPIRE].
G.G. Luciano and A. Sheykhi, Black hole geometrothermodynamics and critical phenomena: A look from Tsallis entropy-based perspective, Phys. Dark Univ. 42 (2023) 101319 [arXiv:2304.11006] [INSPIRE].
S. Basilakos, A. Lymperis, M. Petronikolou and E.N. Saridakis, Alleviating both H0 and σ8 tensions in Tsallis cosmology, arXiv:2308.01200 [INSPIRE].
F. Jüttner, Das maxwellsche gesetz der geschwindigkeitsverteilung in der relativtheorie, Annalen Phys. 339 (1911) 856.
G.G. Luciano, Modified Friedmann equations from Kaniadakis entropy and cosmological implications on baryogenesis and 7Li-abundance, Eur. Phys. J. C 82 (2022) 314 [INSPIRE].
C.H. Nam, Non-linear charged AdS black hole in massive gravity, Eur. Phys. J. C 78 (2018) 1016 [INSPIRE].
G.A. Marks, F. Simovic and R.B. Mann, Phase transitions in 4D Gauss-Bonnet-de Sitter black holes, Phys. Rev. D 104 (2021) 104056 [arXiv:2107.11352] [INSPIRE].
G.-M. Deng, J. Fan, X. Li and Y.-C. Huang, Thermodynamics and phase transition of charged AdS black holes with a global monopole, Int. J. Mod. Phys. A 33 (2018) 1850022 [arXiv:1801.08028] [INSPIRE].
A. Alonso-Serrano, M.P. Dabrowski and H. Gohar, Nonextensive Black Hole Entropy and Quantum Gravity Effects at the Last Stages of Evaporation, Phys. Rev. D 103 (2021) 026021 [arXiv:2009.02129] [INSPIRE].
A. Alonso-Serrano, M.P. Dabrowski and H. Gohar, Minimal length and the flow of entropy from black holes, Int. J. Mod. Phys. D 27 (2018) 1847028 [arXiv:1805.07690] [INSPIRE].
Z.-W. Feng, X. Zhou, S.-Q. Zhou and D.-D. Feng, Rainbow gravity corrections to the information flux of a black hole and the sparsity of Hawking radiation, Annals Phys. 416 (2020) 168144 [arXiv:1808.09958] [INSPIRE].
J.-Y. Shen, R.-G. Cai, B. Wang and R.-K. Su, Thermodynamic geometry and critical behavior of black holes, Int. J. Mod. Phys. A 22 (2007) 11 [gr-qc/0512035] [INSPIRE].
R. Mrugała, On equivalence of two metrics in classical thermodynamics, Physica A 125 (1984) 631.
P.T. Landsberg and V. Vedral, Distributions and channel capacities in generalized statistical mechanics, Phys. Lett. A 247 (1998) 211.
J.-L. Jing, H.-W. Yu and Y.-J. Wang, Thermodynamics of a black hole with a global monopole, Phys. Lett. A 178 (1993) 59 [INSPIRE].
H.-W. Yu, Black hole thermodynamics and global monopoles, Nucl. Phys. B 430 (1994) 427 [INSPIRE].
X.-Z. Li and J.-G. Hao, Global monopole in asymptotically dS / AdS space-time, Phys. Rev. D 66 (2002) 107701 [hep-th/0210050] [INSPIRE].
Q.-Q. Jiang and S.-Q. Wu, Hawking radiation of charged particles as tunneling from Reissner-Nordström-de Sitter black holes with a global monopole, Phys. Lett. B 635 (2006) 151 [hep-th/0511123] [INSPIRE].
T.R.P. Caramês, J.C. Fabris, E.R. Bezerra de Mello and H. Belich, f(R) global monopole revisited, Eur. Phys. J. C 77 (2017) 496 [arXiv:1706.02782] [INSPIRE].
T. Papanikolaou, A. Lymperis, S. Lola and E.N. Saridakis, Primordial black holes and gravitational waves from non-canonical inflation, JCAP 03 (2023) 003 [arXiv:2211.14900] [INSPIRE].
S. Basilakos et al., Gravitational wave signatures of no-scale Supergravity in NANOGrav and beyond, arXiv:2307.08601 [INSPIRE].
S. Mignemi, Extended uncertainty principle and the geometry of (anti)-de Sitter space, Mod. Phys. Lett. A 25 (2010) 1697 [arXiv:0909.1202] [INSPIRE].
J. Giné and G.G. Luciano, Modified inertia from extended uncertainty principle(s) and its relation to MoND, Eur. Phys. J. C 80 (2020) 1039 [INSPIRE].
Acknowledgments
The authors are grateful to the anonymous Reviewer for very helpful suggestions and comments to the original manuscript. GGL would like to thank Jaume Giné, Luca Smaldone and Luca Buoninfante for useful discussions. He is also grateful to the Spanish “Ministerio de Universidades” for the awarded Maria Zambrano fellowship and funding received from the European Union — NextGenerationEU. The authors acknowledge the contribution of the LISA CosWG and of COST Actions CA18108 “Quantum Gravity Phenomenology in the multi-messenger approach” and CA21136 “Addressing observational tensions in cosmology with systematics and fundamental physics (CosmoVerse)”.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
ArXiv ePrint: 2308.12669
Rights and permissions
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.
About this article
Cite this article
Luciano, G.G., Saridakis, E.N. P − v criticalities, phase transitions and geometrothermodynamics of charged AdS black holes from Kaniadakis statistics. J. High Energ. Phys. 2023, 114 (2023). https://doi.org/10.1007/JHEP12(2023)114
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP12(2023)114