Legendre transformations and the thermodynamic geometry of 5D black holes

Abstract

This paper studies the thermodynamic properties of the 5D black hole in Einstein-Gauss-Bonnet gravity from the viewpoint of geometrothermodynamics. It is found that the Legendre invariant metrics of the 5D black holes in Einstein-Yang-Mills-Gauss-Bonnet theory and Einstein-Maxwell-Gauss-Bonnet theory reproduce the behavior of the thermodynamic interaction and phase transition structure of the corresponding black hole configurations correctly. It is shown that they are both curved and that the curvature scalar provides information about the phase transition point.

Thermodynamics and Geometry of Strange Quark Matter

“…We need the fundamental equation Φ = Φ(E a ). We believe the metric given by (27) is a useful tool to study the phase transitions in thermodynamical systems and the black holes and using this approach most of the critical points and even those ones that cannot be obtained by Davis's approach [24] can be obtained as well [25].…”

Thermodynamic Properties of a Regular Black Hole in Gravity Coupling to Nonlinear Electrodynamics

“…The curvature scalar of the Ruppeiner geometry is related to the correlation volume of a thermodynamic system, and its divergent point is the critical point of the thermodynamic phase transition. The properties of the thermodynamic geometries of the black hole have been widely studied [ 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23 , 24 , 25 , 26 , 27 , 28 , 29 , 30 , 31 , 32 , 33 , 34 , 35 , 36 , 37 , 38 ]. It has been found that the Ruppeiner thermodynamic geometry of the Reissner–Nordström (RN) black hole is flat [ 37 ].…”

Dirac equation of spin particles and tunneling radiation from a Kinnersly black hole

“…By taking into account the background change before and after tunneling radiation, they have carried out modification a e-mail: gpliphys@yeah.net b e-mail: zwfengphy@163.com c e-mail: LHL51759@126.com d e-mail: xtzu@uestc.edu.cn to the previous tunneling probability [9]. In recent years, a series of significant studies have been made on the tunneling radiation of black holes [3,[10][11][12][13][14][15][16][17]. Zhang and Zhao et al have developed this tunneling theory, and they studied the relationship between the tunneling radiation and the black hole entropy, which provided a reasonable explanation for the information loss paradox of a black hole [18,19].…”

“…Therefore, information loss paradox of a black hole still needs further research. According to the literature [12][13][14][15][16][17][18][19][20][21][22], the Hamilton-Jacobi equation in curved space-time is the basic equation describing the dynamic characteristics of all kinds of particles. For the Dirac equation describing the spin particle and the equation describing the spin 3/2 particle, the Dirac equation and the tunneling radiation of a stationary black hole have been studied.…”