Geometrothermodynamics of higher dimensional black holes. (English) Zbl 1273.83090

Bravetti, Alessandro; Momeni, Davood; Myrzakulov, Ratbay; Quevedo, Hernando

Gen. Relativ. Gravitation 45, No. 8, 1603-1617 (2013).

Summary: We study the thermodynamics and geometrothermodynamics of different black hole configurations in more than four spacetime dimensions. We use the response functions to find the conditions under which second order phase transitions occur in higher-dimensional static Reissner-Nordström and stationary Kerr black holes. Our results indicate that the equilibrium manifold of all these black hole configurations is in general curved and that curvature singularities appear exactly at those places where second order phase transitions occur.

MSC:

83C57	Black holes
83E15	Kaluza-Klein and other higher-dimensional theories
83E05	Geometrodynamics and the holographic principle
80A10	Classical and relativistic thermodynamics
83C22	Einstein-Maxwell equations

Keywords:

black hole thermodynamics; phase transitions; geometrothermodynamics; Reissner-Nordström; Kerr black holes

References:

[1]	Frankel, T.: The Geometry of Physics: An Introduction. Cambridge University Press, Cambridge (1997) · Zbl 0888.58077
[2]	Gibbs, J.W.: The Collected Works, Vol. 1, Thermodynamics. Yale University Press, New Haven (1948) · Zbl 0031.13504
[3]	Caratheodory, C.: Untersuchungen über die Grundlagen der Thermodynamik. Math. Ann. 67, 355 (1909)
[4]	Rao, CR, No article title, Bull. Calcutta Math. Soc., 37, 81 (1945) · Zbl 0063.06420
[5]	Amari, S.: Differential-Geometrical Methods in Statistics. Springer, Berlin (1985) · Zbl 0559.62001
[6]	Åman, J.E., Bengtsson, I., Pidokrajt, N.: Gen. Relativ. Gravit. 35, 1733 (2003)
[7]	Åman, JE; Pidokrajt, N., No article title, Phys. Rev. D, 73, 024017 (2006)
[8]	Åman, J.E., Pidokrajt, N.: Gen. Relativ. Gravit. 38, 1305 (2006)
[9]	Shen, J., Cai, R.G., Wang, B., Su, R.K.: [gr-qc/0512035]
[10]	Cai, RG; Cho, JH, No article title, Phys. Rev. D, 60, 067502 (1999)
[11]	Sarkar, T.; Sengupta, G.; Tiwari, BN, No article title, J. High Energy Phys., 0611, 015 (2006)
[12]	Medved, AJM, No article title, Mod. Phys. Lett. A, 23, 2149 (2008) · Zbl 1149.83320
[13]	Mirza, B.; Zamaninasab, M., No article title, JHEP, 0706, 059 (2007)
[14]	Quevedo, H.: Gen. Relativ. Gravit. 40, 971 (2008)
[15]	Callen, H.B.: Thermodynamics and An Introduction to Thermostatics. Wiley, New York (1985) · Zbl 0989.80500
[16]	Quevedo, H., No article title, J. Math. Phys., 48, 013506 (2007) · Zbl 1121.80011
[17]	Hermann, R.: Geometry, Physics and Systems. Marcel Dekker, New York (1973) · Zbl 0285.58001
[18]	Quevedo, H., Sánchez, A., Taj, S., Vázquez, A.: Gen. Relativ. Gravit. 43, 1153 (2011)
[19]	Emparan, R.; Reall, HS, No article title, Living Rev. Rel., 11, 6 (2008)
[20]	Gergely, L.; Pidokrajt, N.; Winitzki, S., No article title, Eur. Phys. J. C, 71, 1569 (2011)
[21]	Banerjee, R.; Roychowdhury, D., No article title, JHEP, 1111, 004 (2011) · Zbl 1306.83037
[22]	Banerjee, R.; Modak, SK; Roychowdhury, D., No article title, JHEP, 1210, 125 (2012)
[23]	Banerjee, R.; Ghosh, S.; Roychowdhury, D., No article title, Phys. Lett. B, 696, 156 (2011)
[24]	Quevedo, H.; Sánchez, A., No article title, JHEP, 09, 034 (2008) · Zbl 1245.83037
[25]	Konoplya, RA; Zhidenko, A., No article title, Phys. Rev. Lett., 103, 161101 (2009)
[26]	Arnold, V.I.: Mathematical Methods of Classical Mechanics. Springer, New York (1980)
[27]	Davies, PCW, No article title, Rep. Prog. Phys., 41, 1313 (1978)
[28]	Emparan, R.; Myers, RC, No article title, JHEP, 09, 025 (2003)
[29]	Bravetti, A., Nettel, F.: Second order phase transitions and thermodynamic geometry: a general approach. arXiv:1208.0399