Abstract
In this paper, we consider three types (static, static charged and rotating charged) of black holes in f(R) gravity. We study the thermodynamical behavior, stability conditions and phase transition of these black holes. It will be shown that, the number and type of phase transition points are related to different parameters, which shows the dependency of stability conditions to these parameters. Also, we extended our study to different thermodynamic geometry methods (Ruppeiner, Weinhold and GTD). Next, we investigate the compatibility of curvature scalar of geothermodynamic methods with phase transition points of the above balck holes. In addition, we point out the effect of different values of spacetime parameters on stability conditions of mentioned black holes.
Highlights
GiWj = ∂i ∂ j M(S, N r ), (1)where M is the mass, S is the entropy, and N r is for the other extensive variables of the system
We point out the effect of different values of the spacetime parameters on the stability conditions of this black hole
We studied the thermodynamic behavior of three types of black holes in f (R) gravity, and we investigated the thermodynamic geometry of them
Summary
Where M is the mass, S is the entropy, and N r is for the other extensive variables of the system. In 1979, Ruppeiner [13] defined a new metric which is the minus signed Hessian in the entropy representation and is given by giRj = −∂i ∂ j S(M, N r ). The Ruppeiner metric is conformally related to Weinhold’s metric as follows [14,15]: ds
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