×

The geometry of the higher dimensional black hole thermodynamics in Einstein-Gauss-Bonnet theory. (English) Zbl 1189.83073

Summary: In this paper, we have studied the geometry of the five-dimensional black hole solutions in (a) Einstein-Yang-Mills-Gauss-Bonnet theory and (b) Einstein-Maxwell-Gauss-Bonnet theory with a cosmological constant for spherically symmetric space time. Formulating the Ruppeiner metric, we have examined the possible phase transition for both the metrics. It is found that depending on some restrictions phase transition is possible for the black holes. Also for \(\Lambda = 0\) in Einstein-Gauss-Bonnet black hole, the Ruppeiner metric becomes flat and hence the black hole becomes a stable one.

MSC:

83D05 Relativistic gravitational theories other than Einstein’s, including asymmetric field theories
83C57 Black holes
83E15 Kaluza-Klein and other higher-dimensional theories
83C22 Einstein-Maxwell equations
83C15 Exact solutions to problems in general relativity and gravitational theory
80A10 Classical and relativistic thermodynamics
81T13 Yang-Mills and other gauge theories in quantum field theory
PDFBibTeX XMLCite
Full Text: DOI arXiv

References:

[1] Hawking S.W.: Commun. Math. Phys. 43, 199 (1975) · Zbl 1378.83040
[2] Bekenstein J.D.: Phys. Rev. D 7, 2333 (1973) · Zbl 1369.83037
[3] Bardeen J.M., Carter B., Hawking S.W.: Commun. Math. Phys. 31, 161 (1973) · Zbl 1125.83309
[4] Hut P.: Mon. Not. R. Astron Soc. 180, 379 (1977)
[5] Davies P.C.W.: Proc. Roy. Soc. Lond. A 353, 499 (1977)
[6] Davies P.C.W.: Rep. Prog. Phys. 41, 1313 (1977)
[7] Davies P.C.W.: Class. Quant. Grav. 6, 1909 (1989)
[8] Weinhold F.: J. Chem. Phy. 63, 2479 (1975)
[9] Ruppeiner G.: Rev. Mod. Phys. 67, 605 (1995)
[10] Ruppeiner G.: Rev. Mod. Phys. 68, 313(E) (1996)
[11] Ruppeiner G.: Phys. Rev. A 20, 1608 (1979)
[12] Candelas P., Horowitz G.T., Strominger A., Witten E.: Nucl. Phys. B 258, 46 (1985)
[13] Greens M.B., Schwarz J.H., Witten E.: Superstring Theory. Cambridge University Press, Cambridge (1987)
[14] Polchinski J.: Sting Theory. Cambridge University Press, Cambridge (1998) · Zbl 1006.81522
[15] Zwiebach B.: Phys. Lett. B 156, 315 (1985)
[16] Zumino B.: Phys. Rep. 137, 109 (1986)
[17] Lovelock D.: J. Math. Phys. 12, 498 (1971) · Zbl 0213.48801
[18] Lanczos C.: Ann. Math. 39, 842 (1938) · Zbl 0019.37904
[19] Chamseddine A.H.: Phys. Lett. B 233, 291 (1989) · Zbl 1332.81131
[20] Muller-Hoissen F.: Nucl. Phys. B 349, 235 (1990)
[21] Sami, M., Dadhich, N.: TSPU Vestnik 44N7, 25 (2004)(arXiv:hep-th/0405016)
[22] Mazharimousavi S.H., Halilsoy M.: Phys. Rev. D 76, 087501 (2007)
[23] Aman J., Bengtsson I., Pidokrajt N.: Gen. Relativ. Gravit. 35, 1733 (2003) · Zbl 1034.83011
[24] Falcke, H., Hehl, F.W. (eds.): The Galactic Black Hole: Lectures on General Relativity and Astrophysics. Institute of Physics Publishing, Bristol (2003)
[25] Boulware D.G., Deser S.: Phys. Rev. Lett. 55, 2656 (1985)
[26] Wiltshire D.L.: Phys. Letts. B 169, 36 (1986)
[27] Wiltshire D.L.: Phys. Rev. D 38, 2445 (1988)
[28] Thibeault M., Simeone C., Eirod E.F.: Gen. Relativ. Gravit. 38, 1593 (2006) · Zbl 1117.83029
[29] Quevedo H., Sanchez A.: JHEP 09, 034 (2008) · Zbl 1245.83037
[30] Mirza B., Zamani-Nasab M., Ruppeiner G.: JHEP 0706, 059 (2007)
[31] Quevedo H., Sanchez A.: Phys. Rev. D 79, 024012 (2009) · Zbl 1222.83113
[32] Chakraborty S., Bandyopadhyay T.: Class. Quant. Grav. 25, 245015 (2008) · Zbl 1156.83313
[33] Quevedo H.: J. Math. Phys. 48, 013506 (2007) · Zbl 1121.80011
[34] Alvarez J.L. et al.: Phys. Rev. D 77, 084004 (2008)
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.