Abstract
We study the thermodynamics of black holes (BHs) with a Gauss–Bonnet correction term in ( \(3+1\) )-dimensional AdS space-time. It is known that this term has no effect on the equations of motion, however, it modifies the entropy which is calculated using Wald’s formula. The corrections to the area law appear in the form of a term involving the Gauss–Bonnet parameter. We study charged BHs, namely, Reissner-Nordström and Born–Infeld, under this regime. The first thing we encounter are divergences in heat capacity. After eliminating the possibility of first-order phase transition, we apply two well trusted methods from standard thermodynamics, namely, the Ehrenfest scheme and the Ruppeiner state space geometry analysis to ensure the second-order nature of the phase transition points. Our main focus in this study is on the effects of the Gauss–Bonnet and Born–Infeld parameters on the phase transition points.
