×

Phase transition grade and microstructure of AdS black holes in massive gravity. (English) Zbl 1507.83054

Summary: Considering that under the framework of the massive gravity theory, the interaction between the mass gravitons and Schwarzschild black hole (BH) could make it carry a scalar charge, the phase transition process caused by this scalar charge is investigated in this analysis. The phase transition grade and microstructure of those BHs are investigated from both macroscopic and microscopic points of view. From the macroscopic point of view, it is found that Ehrenfest equations are satisfied at the phase transition critical point, which implies that the phase transition grade of those BHs is second-order. Based on the BH molecules model and Landau continuous phase transition theory, the phase transition of those BHs from the microcosmic point of view is analyzed. The critical exponents obtained from the two perspectives are consistent. By investigating the Ruppeiner geometry, the microstructure feature of those BHs is revealed. These results suggest that the phase transition of BH in massive gravity is a standard second-order phase transition at the critical point, and the microscopic details of those BHs are different from the Reissner-Nordström AdS BH in standard Einstein gravity.

MSC:

83C57 Black holes
82B26 Phase transitions (general) in equilibrium statistical mechanics
74N15 Analysis of microstructure in solids
81V25 Other elementary particle theory in quantum theory
35B33 Critical exponents in context of PDEs
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Abbott, B. P.; LIGO Scientific and Virgo Collaborations; Abbott, B. P.; LIGO Scientific and Virgo Collaborations, Tests of general relativity with GW150914. Tests of general relativity with GW150914, Phys. Rev. Lett.. Phys. Rev. Lett., 121 (2018) · doi:10.1103/physrevlett.121.129902
[2] Fierz, M.; Pauli, W., On relativistic wave equations for particles of arbitrary spin in an electromagnetic field, Proc. R. Soc. A, 173, 211-232 (1939) · Zbl 0023.43004 · doi:10.1098/rspa.1939.0140
[3] van Dam, H.; Veltman, M., Massive and massless Yang-Mills and gravitational fields, Nucl. Phys. B, 22, 397-411 (1970) · doi:10.1016/0550-3213(70)90416-5
[4] Zakharov, V. I., Linearized gravitation theory and the graviton mass, JETP Lett., 12, 312 (1970)
[5] Vainshtein, A. I., To the problem of nonvanishing gravitation mass, Phys. Lett. B, 39, 393-394 (1972) · doi:10.1016/0370-2693(72)90147-5
[6] Boulware, D. G.; Deser, S., Can gravitation have a finite range?, Phys. Rev. D, 6, 3368 (1972) · doi:10.1103/physrevd.6.3368
[7] Arkani-Hamed, N.; Georgi, H.; Schwartz, M. D., Effective field theory for massive gravitons and gravity in theory space, Ann. Phys., NY, 305, 96 (2003) · Zbl 1022.81035 · doi:10.1016/s0003-4916(03)00068-x
[8] Damour, T.; Kogan, I. I.; Papazoglou, A., Spherically symmetric spacetimes in massive gravity, Phys. Rev. D, 67 (2003) · Zbl 1222.83044 · doi:10.1103/physrevd.67.064009
[9] Dubovsky, S. L., Phases of massive gravity, J. High Energy Phys. (2004) · doi:10.1088/1126-6708/2004/10/076
[10] Hooft, G., Unitarity in the Brout-Englert-Higgs mechanism for gravity (2007)
[11] Bebronne, M. V.; Tinyakov, P. G., Black hole solutions in massive gravity, J. High Energy Phys. (2009) · doi:10.1088/1126-6708/2009/04/100
[12] Hawking, S. W.; Page, D. N., Thermodynamics of black holes in anti-de Sitter space, Commun. Math. Phys., 87, 577 (1983) · doi:10.1007/bf01208266
[13] Witten, E., Anti-de Sitter space, thermal phase transition, and confinement in gauge theories, Adv. Theor. Math. Phys., 2, 505-532 (1998) · Zbl 1057.81550 · doi:10.4310/atmp.1998.v2.n3.a3
[14] Landsteiner, K., String corrections to the Hawking-Page phase transition, mode, Phys. Let. A, 14, 379-385 (1999) · doi:10.1142/s0217732399000432
[15] Stephens, G. J.; Hu, B. L., Notes on black hole phase transitions, Int. J. Theor. Phys., 40, 2183-2200 (2001) · Zbl 0987.83035 · doi:10.1023/a:1012930019453
[16] Birmingham, D.; Sachs, I.; Solodukhin, S. N., Relaxation in conformal field theory, Hawking-Page transition, and quasinormal or normal modes, Phys. Rev. D, 67 (2003) · doi:10.1103/physrevd.67.104026
[17] Chamblin, A.; Karch, A., Hawking-Page phase transition on the brane, Phys. Rev. D, 72 (2005) · doi:10.1103/physrevd.72.066011
[18] Kajantie, K.; Tahkokallio, T.; Yee, J-T, Thermodynamics of AdS/QCD, J. High Energy Phys. (2007) · doi:10.1088/1126-6708/2007/01/019
[19] Kastor, D.; Ray, S.; Traschen, J., Enthalpy and the mechanics of AdS black holes, Class. Quantum Grav., 26 (2009) · Zbl 1178.83030 · doi:10.1088/0264-9381/26/19/195011
[20] Akbar, M. M., Schwarzschild-anti-de Sitter black holes within isothermal cavity: thermodynamics, phase transitions, and the Dirichlet problem, Phys. Rev. D, 82 (2010) · doi:10.1103/physrevd.82.064001
[21] Kubizňák, D.; Mann, R. B., P-V criticality of charged AdS black holes, J. High Energy Phys. (2012) · Zbl 1397.83072 · doi:10.1007/JHEP07(2012)033
[22] Spallucci, E.; Smailagic, A., Maxwell s equal-area law for charged anti-de Sitter black holes, Phys. Lett. B, 723, 436 (2013) · Zbl 1311.83028 · doi:10.1016/j.physletb.2013.05.038
[23] Hendi, S. H.; Vahidinia, M. H., Extended phase space thermodynamics and P-V criticality of black holes with nonlinear source, Phys. Rev. D, 88 (2013) · doi:10.1103/physrevd.88.084045
[24] Hendi, S. H.; Panahiyan, S.; Panah, B. E., P-V criticality and geometrical thermodynamics of black holes with Born-Infeld type nonlinear electrodynamics, Int. J. Mod. Phys. D, 25, 1650010 (2014) · Zbl 1337.83039 · doi:10.1142/s0218271816500103
[25] Mo, J-X; Liu, W-B, Ehrenfest scheme for P-V criticality of higher dimensional charged black holes, rotating black holes, and Gauss-Bonnet AdS black holes, Phys. Rev. D, 89 (2014) · doi:10.1103/physrevd.89.084057
[26] Guo, S.; Liang, E-W, Ehrenfest’s scheme and microstructure for regular-AdS black hole in the extended phase space, Class. Quantum Grav., 38 (2021) · Zbl 1480.83081 · doi:10.1088/1361-6382/abf9b6
[27] Ökcü, Ö.; Aydıner, E., Joule-Thomson expansion of the charged AdS black holes, Eur. Phys. J. C, 77, 24 (2017) · doi:10.1140/epjc/s10052-017-4598-y
[28] Guo, S.; Pu, J.; Jiang, Q-Q; Zu, X-T, Joule-Thomson expansion of the regular(Bardeen)-AdS black hole*, Chin. Phys. C, 44 (2020) · doi:10.1088/1674-1137/44/3/035102
[29] Guo, X-Y; Li, H-F; Zhang, L-C; Zhao, R., Microstructure and continuous phase transition of a Reissner-Nordstrom-AdS black hole, Phys. Rev. D, 100 (2019) · doi:10.1103/physrevd.100.064036
[30] Zhang, J-L; Cai, R-G; Yu, H., Phase transition and thermodynamical geometry for Schwarzschild AdS black hole in AdS_5 × S^5 spacetime, J. High Energy Phys. (2015) · Zbl 1388.83510 · doi:10.1007/jhep02(2015)143
[31] Zhang, J-L; Cai, R-G; Yu, H-W, Phase transition and thermodynamical geometry of Reissner-Nordström-AdS black holes in extended phase space, Phys. Rev. D, 91 (2015) · doi:10.1103/physrevd.91.044028
[32] Wei, S-W; Liu, Y-X; Mann, R. B., Repulsive interactions and universal properties of charged anti-de Sitter black hole microstructures, Phys. Rev. Lett., 123 (2019) · doi:10.1103/physrevlett.123.071103
[33] Wei, S-W; Liu, Y-X; Mann, R. B., Ruppeiner geometry, phase transitions, and the microstructure of charged AdS black holes, Phys. Rev. D, 100 (2019) · doi:10.1103/physrevd.100.124033
[34] Cai, R-G; Hu, Y-P; Pan, Q-Y; Zhang, Y-L, Thermodynamics of black holes in massive gravity, Phys. Rev. D, 91 (2015) · doi:10.1103/physrevd.91.024032
[35] Xu, J.; Cao, L-M; Hu, Y-P, P-V criticality in the extended phase space of black holes in massive gravity, Phys. Rev. D, 91 (2015) · doi:10.1103/physrevd.91.124033
[36] Dolan, B. P., The cosmological constant and black-hole thermodynamic potentials, Class. Quantum Grav., 28 (2011) · Zbl 1219.83135 · doi:10.1088/0264-9381/28/12/125020
[37] Wei, S-W; Liu, Y-X, Insight into the microscopic structure of an AdS black hole from thermodynamical phase transition, Phys. Rev. Lett., 115 (2015) · doi:10.1103/physrevlett.115.111302
[38] Lagos, M.; Bellini, E.; Noller, J.; Ferreira, P. G.; Baker, T., A general theory of linear cosmological perturbations: stability conditions, the quasistatic limit and dynamics, J. Cosmol. Astropart. Phys. (2018) · Zbl 07458466 · doi:10.1088/1475-7516/2018/03/021
[39] Ezquiaga, J. M.; Zumalacárregui, M., Dark energy in light of multi-messenger gravitational-wave astronomy, Front. Astron. Space Sci., 5, 44 (2018) · doi:10.3389/fspas.2018.00044
[40] Mastrogiovanni, S.; Steer, D. A.; Barsuglia, M., Probing modified gravity theories and cosmology using gravitational-waves and associated electromagnetic counterparts, Phys. Rev. D, 102 (2020) · doi:10.1103/physrevd.102.044009
[41] Kruglov, S. I., The shadow of M87* black hole within rational nonlinear electrodynamics, Mod. Phys. Lett. A, 35, 2050291 (2020) · doi:10.1142/s0217732320502910
[42] Allahyari, A.; Khodadi, M.; Vagnozzi, S.; Mota, D. F., Magnetically charged black holes from non-linear electrodynamics and the Event Horizon Telescope, J. Cosmol. Astropart. Phys. (2020) · Zbl 1489.83044 · doi:10.1088/1475-7516/2020/02/003
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.