The geometry of the higher dimensional black hole thermodynamics in Einstein–Gauss–Bonnet theory

Abstract

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) EinsteinMaxwell-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 = 0 in Einstein-Gauss-Bonnet black hole, the Ruppeiner metric becomes flat and hence the black hole becomes a stable one.

Black holes in the Einstein–Gauss–Bonnet theory and the geometry of their thermodynamics—II

“…For both black holes the variation of the thermodynamical parameters (namely mass, temperature and heat capacity) are different from those of our earlier work (Biswas and Chakraborty 2009). The basic difference in the two papers is the choice of the entropy function in the previous paper; the Bekenstein-Hawking entropy relation has been used before, while in the present paper we have chosen the entropy of a Schwarzschild-like black hole in EGB gravity.…”

Geometrothermodynamics of five dimensional black holes in Einstein–Gauss–Bonnet theory

“…Some puzzling results arise also in connection with the use of different metrics in the equilibrium space [16][17][18][19], in the sense that for the same thermodynamic system the resulting geometry can be either flat or curved, depending on the chosen metric. Recently, in the analysis of Einstein-Gauss-Bonnet (EGB) black holes inconsistencies were also found [20][21][22]. In this work, we will focus on the study of EGB black holes and will clarify these inconsistencies.…”

“…The signature, in turn, is fixed by the order of the phase transition under consideration. 1 Since in this work we will analyze second order phase transitions of EGB black holes [20][21][22], we choose the metric as…”

Thermodynamics of d-dimensional charged AdS (Anti-de sitter) black holes: Hamiltonian approach and Clapeyron equation

“…In recent years the thermodynamic aspects of AdS space-times are considered in several references like [7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25]. The thermodynamics of the BHs with cosmological constant Λ as a thermodynamical variable has been studied in the references [26,27,28].…”