Phase Structure of Scalarized Black Holes in Einstein-Scalar-Gauss-Bonnet Gravity

TL;DR

This paper explores the thermodynamic phase transitions of scalarized black holes in Einstein-scalar-Gauss-Bonnet gravity, revealing a complex phase structure influenced by different scalar-Gauss-Bonnet couplings.

Contribution

It provides a detailed analysis of the phase structure of scalarized black holes under various coupling functions, highlighting new thermodynamic behaviors.

Findings

Quadratic coupling leads to no phase transition.

Exponential coupling exhibits various phase transitions depending on parameters.

Nonlinear scalarization can result in first-order transitions or none.

Abstract

We revisit scalarized black holes in Einstein-scalar-Gauss-Bonnet gravity and analyze the thermodynamic phase transition between the Schwarzschild solution of general relativity and scalarized black holes. Restricting to spherically symmetric configurations, we investigate several classes of scalar-Gauss-Bonnet coupling functions. For the simplest quadratic coupling that triggers spontaneous scalarization, the scalarized solutions are thermodynamically disfavored and no phase transition occurs. For an exponential coupling, the phase structure depends strongly on the coupling parameter, allowing for the absence of a transition, a continuous second-order transition, or a discontinuous first-order transition. For couplings leading to purely nonlinear scalarization, we find either a first-order transition or no transition. These results reveal a rich phase structure of scalarized black holes controlled by the scalar-Gauss-Bonnet coupling.