Thermodynamics of a class of non-asymptotically flat black holes in Einstein-Maxwell-dilaton theory. (English) Zbl 1273.83111
Summary: We analyse in detail the thermodynamics in the canonical and grand canonical ensembles of a class of non-asymptotically flat black holes of the Einstein-(anti) Maxwell-(anti) Dilaton theory in 4D with spherical symmetry. We present the first law of thermodynamics, the thermodynamic analysis of the system through the geometrothermodynamics methods, Weinhold, Ruppeiner, Liu-Lu-Luo-Shao and the most common, that made by the specific heat. The geometric methods show a curvature scalar identically zero, which is incompatible with the results of the analysis made by the non null specific heat, which shows that the system is thermodynamically interacting, does not possess extreme case nor phase transition. We also analyse the local and global stability of the thermodynamic system, and obtain a local and global stability for the normal case for \(0 < \gamma < 1\) and for other values of \(\gamma \), an unstable system. The solution where \(\gamma = 0\) separates the class of locally and globally stable solutions from the unstable ones.
MSC:
| 83C57 | Black holes |
| 80A10 | Classical and relativistic thermodynamics |
| 83C25 | Approximation procedures, weak fields in general relativity and gravitational theory |
| 83C22 | Einstein-Maxwell equations |
| 83C15 | Exact solutions to problems in general relativity and gravitational theory |
| 81T20 | Quantum field theory on curved space or space-time backgrounds |
References:
| [1] | Chan, KCK; Horne, JH; Mann, RB, No article title, Nucl. Phys. B, 447, 441-464 (1995) · Zbl 1009.83510 · doi:10.1016/0550-3213(95)00205-7 |
| [2] | Ghosh, T.; Mitra, P., No article title, Class. Quantum Gravity, 20, 1403-1410 (2003) · Zbl 1035.83017 · doi:10.1088/0264-9381/20/7/311 |
| [3] | Kiem, Y., Park, D.: Nucl. Phys. B 486, 114-130 (1997). hep-th/9611178 · Zbl 0925.83067 |
| [4] | Clement, G., Leygnac, C.: Phys. Rev. D 70, 084018 (2004). gr-qc/0405034 |
| [5] | Clement, G., Galtsov, D., Leygnac, C.: Phys. Rev. D 71, 084014 (2005). hep-th/0412321 |
| [6] | Clement, G., Fabris, J.C., Rodrigues, M.E.: Phys. Rev. D 79, 064021 (2009). arXiv:hep-th/09014543 |
| [7] | Marques, G.T., Rodrigues, M.E.: Eur. Phys. J. C 72, 1891 (2012). arXiv:1110.0079 [gr-qc] |
| [8] | Mignemi, S.; Wiltshire, D., No article title, Class. Quantum Gravity, 6, 987 (1989) · Zbl 0669.53064 · doi:10.1088/0264-9381/6/7/006 |
| [9] | Wiltshire, DL, No article title, Phys. Rev. D, 44, 1100 (1991) · doi:10.1103/PhysRevD.44.1100 |
| [10] | Mignemi, S.; Wiltshire, DL, No article title, Phys. Rev. D, 46, 1475 (1992) · doi:10.1103/PhysRevD.46.1475 |
| [11] | Poletti, SJ; Wiltshire, DL, No article title, Phys. Rev. D, 50, 7260 (1994) · doi:10.1103/PhysRevD.50.7260 |
| [12] | Cai, RG; Ji, JY; Soh, KS, No article title, Phys. Rev D, 57, 6547 (1998) · doi:10.1103/PhysRevD.57.6547 |
| [13] | Cai, RG; Zhang, YZ, No article title, Phys. Rev D, 64, 104015 (2001) · doi:10.1103/PhysRevD.64.104015 |
| [14] | Ghosh, T.; Mitra, P., No article title, Class. Quantum Gravity, 20, 1403 (2003) · Zbl 1035.83017 · doi:10.1088/0264-9381/20/7/311 |
| [15] | Sheykhi, A.; Riazi, N., No article title, Int. J. Theor. Phys., 45, 2453 (2006) · Zbl 1117.83078 · doi:10.1007/s10773-006-9213-1 |
| [16] | Dehghani, MH; Farhangkhah, N., No article title, Phys. Rev. D, 71, 044008 (2005) · doi:10.1103/PhysRevD.71.044008 |
| [17] | Dehghani, MH, No article title, Phys. Rev. D, 71, 064010 (2005) · doi:10.1103/PhysRevD.71.064010 |
| [18] | Sheykhi, A.; Dehghani, MH; Riazi, N., No article title, Phys. Rev. D, 75, 044020 (2007) · doi:10.1103/PhysRevD.75.044020 |
| [19] | Sheykhi, A.; Dehghani, MH; Riazi, N.; Pakravan, J., No article title, Phys. Rev. D, 74, 084016 (2006) · doi:10.1103/PhysRevD.74.084016 |
| [20] | Sheykhi, A.; Riazi, N.; Mahzoon, MH, No article title, Phys. Rev. D, 74, 044025 (2006) · doi:10.1103/PhysRevD.74.044025 |
| [21] | Sheykhi, A.: Phys. Rev. D 76, 124025 (2007) |
| [22] | Yazadjiev, SS, No article title, Phys. Rev. D, 72, 044006 (2005) · doi:10.1103/PhysRevD.72.044006 |
| [23] | Yazadjiev, SS, No article title, Class. Quantum Gravity, 22, 3875 (2005) · Zbl 1075.83543 · doi:10.1088/0264-9381/22/19/005 |
| [24] | Clement, G., Gal’tsov, D., Leygnac, C.: Phys. Rev. D 67, 024012 (2003) |
| [25] | Aharony, O.; Berkooz, M.; Kutasov, D.; Seiberg, N., No article title, J. High Energy Phys., 10, 004 (1998) · Zbl 0955.81040 · doi:10.1088/1126-6708/1998/10/004 |
| [26] | Hawking, SW; Page, DN, No article title, Commun. Math. Phys., 87, 577 (1983) · doi:10.1007/BF01208266 |
| [27] | Rao, CR, No article title, Bull. Calcutta Math. Soc., 37, 81 (1945) · Zbl 0063.06420 |
| [28] | Amari, S.: Differential-Geometrical Methods in Statistics. Springer, Berlin (1985) · Zbl 0559.62001 · doi:10.1007/978-1-4612-5056-2 |
| [29] | Weinhold, F.: J. Chem. Phys. 63, 2479, 2484, 2488, 2496 (1975) |
| [30] | Weinhold, F., No article title, J. Chem. Phys., 65, 559 (1976) · doi:10.1063/1.433136 |
| [31] | Ruppeiner, G., No article title, Phys. Rev. A, 20, 1608 (1979) · doi:10.1103/PhysRevA.20.1608 |
| [32] | Ruppeiner, G., No article title, Rev. Mod. Phys., 67, 605 (1995) · doi:10.1103/RevModPhys.67.605 |
| [33] | Ruppeiner, G., No article title, Rev. Mod. Phys., 68, 313 (1996) · doi:10.1103/RevModPhys.68.313 |
| [34] | Quevedo, H., No article title, J. Math. Phys., 48, 013506 (2007) · Zbl 1121.80011 · doi:10.1063/1.2409524 |
| [35] | Quevedo, H.: Gen. Relativ. Gravit. 40, 971-984 (2008). arXiv:1111.5056 [math-ph] · Zbl 1140.83398 |
| [36] | Liu, H., Lu, H., Luo, M., Shao, K.-N.: JHEP 1012, 054 (2010). arXiv:1008.4482 [hep-th] |
| [37] | Jardim, D.F., Rodrigues, M.E., Houndjo, S.J.M.: arXiv:1202.2830v2 [gr-qc] |
| [38] | Booth, I.S.N.: A quasilocal Hamiltonian for gravity with classical and quantum applications. Ph.D. thesis. gr-qc/0008030 |
| [39] | Gibbons, GW; Hawking, S., No article title, Phys. Rev. D, 15, 2752-2756 (1977) · doi:10.1103/PhysRevD.15.2752 |
| [40] | Hawking, S., No article title, Commun. Math. Phys., 43, 199 (1975) · Zbl 1378.83040 · doi:10.1007/BF02345020 |
| [41] | Birrell, N.D., Davies, P.C.W.: Quantum Fields in Curved Space. Cambridge University Press, Cambridge (1982) · Zbl 0476.53017 · doi:10.1017/CBO9780511622632 |
| [42] | Ford, L.H.: arXiv: gr-qc/9707062 |
| [43] | Davies, PCW, No article title, Proc. R. Soc. Lond. A, 353, 499-521 (1977) · doi:10.1098/rspa.1977.0047 |
| [44] | Clement, G.; Fabris, JC; Marques, GT, No article title, Phys. Lett. B, 651, 54-57 (2007) · Zbl 1248.83053 · doi:10.1016/j.physletb.2007.05.052 |
| [45] | Kanti, P.; March-Russell, J., No article title, Phys. Rev. D, 66, 024023 (2002) · doi:10.1103/PhysRevD.66.024023 |
| [46] | Kim, W.; Oh, JJ, No article title, J. Korean Phys. Soc., 52, 986 (2008) · doi:10.3938/jkps.52.986 |
| [47] | Ghoroku, K.; Larsen, AL, No article title, Phys. Lett. B, 328, 28-35 (1994) · doi:10.1016/0370-2693(94)90423-5 |
| [48] | Robinson, SP; Wilczek, F., No article title, Phys. Rev. Lett., 95, 011303 (2005) · doi:10.1103/PhysRevLett.95.011303 |
| [49] | Jacobson, T., Kang, G.: Class. Quantum Gravity 10, L201-L206 (1993). arXiv: gr-qc/9307002 · Zbl 0794.53056 |
| [50] | Wald, R.M.: Genaral Relativity. University of Chicago Press, Chicago (1984) · Zbl 0549.53001 · doi:10.7208/chicago/9780226870373.001.0001 |
| [51] | Clement, G., No article title, Phys. Rev. D, 68, 024032 (2003) · doi:10.1103/PhysRevD.68.024032 |
| [52] | Hermann, R.: Geometry, Physics, Systems. Marcel Dekker, New York (1973) · Zbl 0285.58001 |
| [53] | Hernandez, G., Lacomba, E.A.: Contact Riemannian geometry, thermodynamics. Diff. Geom. Appl. 8, 205 (1998) · Zbl 0947.53040 · doi:10.1016/S0926-2245(98)00006-0 |
| [54] | Rodrigues, M.E., Oporto, Z.A.A.: Phys. Rev. D 85, 104022 (2012). arXiv:1201.5337v3 [gr-qc] |
| [55] | Cao, Q.-J., Chen, Y.-X., Shao, K.-N.: Phys. Rev. D 83, 064015 (2011). arXiv:1010.5044v2 [hep-th] |
| [56] | Sheykhi, A., Dehghani, M.H., Hendi, S.H.: Phys. Rev. D 81, 084040 (2010) |
| [57] | Hendi, S.H., Sheykhi, A., Dehghani, M.H.: Eur. Phys. J. C 70, 703-712 (2010) |
| [58] | Myung, Y.S.: Phys. Lett. B 624, 297-303 (2005) · Zbl 1247.83143 |
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.
