More on phase transition and Rényi entropy

Abstract

In this paper, we study the scalar field condensation around the hyperbolic black hole solutions in the Einstein and Gauss–Bonnet gravities. We investigate the Rényi entropy and inequalities governing on it under this phase transition. Our numerical computations show that for the positive values of the Gauss–Bonnet coupling and below a critical temperature one of these inequalities is violated. This puts more restrictions on the allowed values of the Gauss–Bonnet coupling.