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Thermodynamic analysis of black hole solutions in gravitating nonlinear electrodynamics. (English) Zbl 1274.83023

Summary: We perform a general study of the thermodynamic properties of static electrically charged black hole solutions of nonlinear electrodynamics minimally coupled to gravitation in three space dimensions. The Lagrangian densities governing the dynamics of these models in flat space are defined as arbitrary functions of the gauge field invariants, constrained by some requirements for physical admissibility. The exhaustive classification of these theories in flat space, in terms of the behaviour of the Lagrangian densities in vacuum and on the boundary of their domain of definition, defines twelve families of admissible models. When these models are coupled to gravity, the flat space classification leads to a complete characterization of the associated sets of gravitating electrostatic spherically symmetric solutions by their central and asymptotic behaviours. We focus on nine of these families, which support asymptotically Schwarzschild-like black hole configurations, for which the thermodynamic analysis is possible and pertinent. In this way, the thermodynamic laws are extended to the sets of black hole solutions of these families, for which the generic behaviours of the relevant state variables are classified and thoroughly analyzed in terms of the aforementioned boundary properties of the Lagrangians. Moreover, we find universal scaling laws (which hold and are the same for all the black hole solutions of models belonging to any of the nine families) running the thermodynamic variables with the electric charge and the horizon radius. These scale transformations form a one-parameter multiplicative group, leading to universal “renormalization group”-like first-order differential equations. The beams of characteristics of these equations generate the full set of black hole states associated to any of these gravitating nonlinear electrodynamics. Moreover the application of the scaling laws allows to find a universal finite relation between the thermodynamic variables, which is seen as a generalized Smarr law. Some particular well known (and also other new) models are analyzed as illustrative examples of these procedures.

MSC:

83C15 Exact solutions to problems in general relativity and gravitational theory
80A10 Classical and relativistic thermodynamics
83C57 Black holes
78A25 Electromagnetic theory (general)
83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
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[1] Carter, B.: Phys. Rev. Lett. 26, 331 (1971)
[2] Penrose, R., No article title, Riv. Nuovo Cim. Numero Speciale, 1, 252 (1969)
[3] Penrose, R., No article title, Gen. Relativ. Gravit., 34, 1141 (2002) · Zbl 1001.83040 · doi:10.1023/A:1016578408204
[4] Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973) · Zbl 0265.53054 · doi:10.1017/CBO9780511524646
[5] Misner, C.W., Thorne, K.S., Wheeler, J.A.: Gravitation. W. H. Freeman, San Francisco (1973)
[6] Fradkin, E.; Tseytlin, AA, No article title, Phys. Lett. B, 163, 123 (1985) · Zbl 0967.81534 · doi:10.1016/0370-2693(85)90205-9
[7] Abouelsaood, A.; Callan, CG; Nappi, CR; Yost, SA, No article title, Nucl. Phys. B, 280, 599 (1987) · doi:10.1016/0550-3213(87)90164-7
[8] Leigh, RG, No article title, Mod. Phys. Lett. A, 4, 2767 (1989) · doi:10.1142/S0217732389003099
[9] Brecher, D., No article title, Phys. Lett. B, 442, 117 (1998) · Zbl 1002.81539 · doi:10.1016/S0370-2693(98)01277-5
[10] Brecher, D.; Perry, MJ, No article title, Nucl. Phys. B, 527, 121 (1998) · Zbl 0951.81027 · doi:10.1016/S0550-3213(98)00297-1
[11] Tseytlin, AA, No article title, Nucl. Phys. B, 501, 41 (1997) · Zbl 0939.81030 · doi:10.1016/S0550-3213(97)00354-4
[12] Born, M.; Infeld, L., No article title, Proc. R. Soc. Lond. A, 144, 425 (1934) · Zbl 0008.42203 · doi:10.1098/rspa.1934.0059
[13] Dyadichev, VV; Gal’tsov, DV; Zorin, AG; Zotov, MY, No article title, Phys. Rev. D, 65, 084007 (2002) · doi:10.1103/PhysRevD.65.084007
[14] Füzfa, A.; Alimi, J-M, No article title, Phys. Rev. Lett., 97, 061301 (2006) · Zbl 1228.83129 · doi:10.1103/PhysRevLett.97.061301
[15] Füzfa, A.; Alimi, J-M, No article title, Phys. Rev. D, 73, 023520 (2006) · doi:10.1103/PhysRevD.73.023520
[16] Heisenberg, W.; Euler, H., No article title, Z. Phys., 120, 714 (1936)
[17] Schwinger, J., No article title, Phys. Rev., 82, 664 (1951) · Zbl 0043.42201 · doi:10.1103/PhysRev.82.664
[18] Bialynicka-Birula, Z.; Bialynicki-Birula, I., No article title, Phys. Rev. D, 2, 2341 (1970) · doi:10.1103/PhysRevD.2.2341
[19] Diaz-Alonso, J.; Rubiera-Garcia, D., No article title, Ann. Phys., 324, 827 (2009) · Zbl 1168.70012 · doi:10.1016/j.aop.2008.09.008
[20] Dobado, A., Gómez-Nicola, A., Maroto, A.L., Peláez, J.R.: Effective Lagrangians for the Standard Model. Springer, Berlin (1997) · Zbl 0888.58076 · doi:10.1007/978-3-642-59191-4
[21] Buchbinder, I.L., Odintsov, S.D., Shapiro, I.L.: Effective Action in Quantum Gravity. IOP Publishing Ltd, Bristol, Philadelphia (1992)
[22] Diaz-Alonso, J.; Rubiera-Garcia, D., No article title, Phys. Rev. D, 81, 064021 (2010) · doi:10.1103/PhysRevD.81.064021
[23] Diaz-Alonso, J.; Rubiera-Garcia, D., No article title, Phys. Rev. D, 82, 085024 (2010) · doi:10.1103/PhysRevD.82.085024
[24] Bardeen, JM; Carter, B.; Hawking, S., No article title, Commun. Math. Phys., 31, 161 (1973) · Zbl 1125.83309 · doi:10.1007/BF01645742
[25] Bekenstein, J.D.: Baryon Number, Entropy and Black Hole Physics. Ph.D thesis, Princeton (1972)
[26] Bekenstein, JD, No article title, Phys. Rev. D, 7, 2333 (1973) · Zbl 1369.83037 · doi:10.1103/PhysRevD.7.2333
[27] Hawking, SW, No article title, Nature, 248, 30 (1974) · Zbl 1370.83053 · doi:10.1038/248030a0
[28] Hawking, S.W.: Commun. Math. Phys. 43, 199 (1975) [Erratum ibid. 46, 206 (1976)]
[29] Peca, CS; Lemos, JPS, No article title, Phys. Rev. D, 59, 124007 (1999) · doi:10.1103/PhysRevD.59.124007
[30] Chamblin, A., Emparan, R., Johnson, C.V., Myers, R.C.: Phys. Rev. D 60, 104026 (1999)
[31] Chamblin, A., Emparan, R., Johnson, C.V., Myers, R.C.: Phys. Rev. D 60, 064018 (1999)
[32] Rasheed, D.A.: hep-th/9702087
[33] Chemissany, WA; Roo, M.; Panda, S., No article title, Class. Quant. Gravit., 25, 225009 (2008) · Zbl 1152.83375 · doi:10.1088/0264-9381/25/22/225009
[34] Gonzalez, HA; Hassaine, M.; Martinez, C., No article title, Phys. Rev. D, 80, 104008 (2009) · doi:10.1103/PhysRevD.80.104008
[35] Myung, YS; Kim, Y-W; Park, Y-J, No article title, Gen. Relativ. Gravit., 41, 1051 (2009) · Zbl 1177.83090 · doi:10.1007/s10714-008-0690-9
[36] Dey, TK, No article title, Phys. Lett. B, 595, 484 (2004) · Zbl 1247.83102 · doi:10.1016/j.physletb.2004.06.047
[37] Fernando, S., No article title, Phys. Rev. D, 74, 104032 (2006) · doi:10.1103/PhysRevD.74.104032
[38] Myung, YS; Kim, Y-W; Park, Y-J, No article title, Phys. Rev. D, 78, 084002 (2008) · doi:10.1103/PhysRevD.78.084002
[39] Miskovic, O.; Olea, R., No article title, Phys. Rev. D, 77, 124048 (2008) · doi:10.1103/PhysRevD.77.124048
[40] Banerjee, R.; Roychowdhury, D., No article title, Phys. Rev. D, 85, 104043 (2012) · doi:10.1103/PhysRevD.85.104043
[41] Cai, R-G; Pang, D-W; Wang, A., No article title, Phys. Rev. D, 70, 124034 (2004) · doi:10.1103/PhysRevD.70.124034
[42] Myung, YS; Kim, Y-W; Park, Y-J, No article title, Phys. Rev. D, 78, 044020 (2008) · doi:10.1103/PhysRevD.78.044020
[43] Hawking, SW; Page, DN, No article title, Commun. Math. Phys., 87, 577 (1983) · doi:10.1007/BF01208266
[44] Maldacena, J., No article title, Adv. Theor. Math. Phys., 2, 231 (1998) · Zbl 0914.53047
[45] Maldacena, J., No article title, Int. J. Phys., 38, 1113 (1999) · Zbl 0969.81047 · doi:10.1023/A:1026654312961
[46] Witten, E., No article title, Adv. Theor. Math. Phys., 2, 253 (1998) · Zbl 0914.53048
[47] Gubser, SS; Klebanov, IR; Polyakov, AM, No article title, Phys. Lett. B, 428, 105 (1998) · Zbl 1355.81126 · doi:10.1016/S0370-2693(98)00377-3
[48] Wiltshire, DL, No article title, Phys. Rev. D, 38, 2445 (1988) · doi:10.1103/PhysRevD.38.2445
[49] Aiello, M.; Ferraro, R.; Giribet, G., No article title, Phys. Rev. D, 70, 104014 (2004) · doi:10.1103/PhysRevD.70.104014
[50] Aiello, M.; Ferraro, R.; Giribet, G., No article title, Class. Quant. Gravit., 22, 2579 (2005) · Zbl 1074.83022 · doi:10.1088/0264-9381/22/13/004
[51] Maeda, H.; Hassaine, M.; Martinez, C., No article title, Phys. Rev. D, 79, 044012 (2009) · doi:10.1103/PhysRevD.79.044012
[52] Miskovic, O., Olea, R.: Phys. Rev. D 83, 024011 (2011)
[53] Miskovic, O., Olea, R.: Phys. Rev. D 83, 064017 (2011)
[54] Corda, C.; Mosquera Cuesta, H., No article title, J. Astropart. Phys., 34, 587 (2011) · doi:10.1016/j.astropartphys.2010.12.002
[55] Olmo, GJ; Rubiera-Garcia, D., No article title, Phys. Rev. D, 84, 124059 (2011) · doi:10.1103/PhysRevD.84.124059
[56] Mazharimousavi, H.; Halilsoy, M.; Tahamtan, T., No article title, Eur. Phys. J. C, 72, 185 (2012)
[57] Doneva, DD; Yazadjiev, SS; Kokkotas, KD, No article title, Phys. Rev. D, 81, 104030 (2010) · doi:10.1103/PhysRevD.81.104030
[58] Strominger, A.; Vafa, C., No article title, Phys. Lett. B, 379, 99 (1996) · Zbl 1376.83026 · doi:10.1016/0370-2693(96)00345-0
[59] Callan, CG; Maldacena, JM, No article title, Nucl. Phys. B, 472, 591 (1996) · Zbl 0925.83041 · doi:10.1016/0550-3213(96)00225-8
[60] Ortin, T.: Gravity and Strings, Cambridge Monographs on Mathematical Physics. C.U.P, Cambridge (2004) · Zbl 1057.83003 · doi:10.1017/CBO9780511616563
[61] Soleng, HH, No article title, Phys. Rev. D, 52, 6178 (1995) · doi:10.1103/PhysRevD.52.6178
[62] Boyer, RH, No article title, Proc. R. Soc. Lond. A, 311, 245 (1969) · Zbl 0193.27902 · doi:10.1098/rspa.1969.0116
[63] Lala, A.; Roychowdhuy, R., No article title, Phys. Rev. D, 86, 084027 (2012) · doi:10.1103/PhysRevD.86.084027
[64] Yajima, H.; Tamaki, T., No article title, Phys. Rev. D, 63, 064007 (2001) · doi:10.1103/PhysRevD.63.064007
[65] Smarr, L., No article title, Phys. Rev. Lett., 30, 71 (1973) · doi:10.1103/PhysRevLett.30.71
[66] Landau, L., Lifchitz, E.: Theories des Champs, Sec. 37. Ed. MIR, Moscou (1970)
[67] Diaz-Alonso, J., Rubiera-Garcia, D.: Proceedings of the NEB14. J. Phys: Conf. Ser. 283, 012014 (2011). IOP Publishing
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