Black holes with non-minimal derivative coupling

TL;DR

This paper explores black hole solutions in a modified gravity theory involving a scalar field coupled to the Einstein tensor, revealing unique thermodynamic behaviors and phase transitions influenced by the Galileon coupling.

Contribution

It provides analytical black hole solutions in a non-minimally coupled scalar-tensor theory and analyzes their thermodynamics and phase transitions.

Findings

Black hole solutions with a regular horizon were found.

The Galileon coupling exhibits non-perturbative effects.

A Hawking-Page-like phase transition was identified.

Abstract

We study the gravitational field equations in the presence of a coupling between the derivative of a massless scalar field and the Einstein tensor. This configuration is motivated by Galileon gravity as it preserves shift invariance in the scalar sector. We analytically obtain solutions with static and spherically symmetric geometry, which also include black holes with a single regular horizon. We examine the thermodynamical properties of these solutions, and we reveal the non-perturbative nature of the Galileon coupling constant. We also find a phase transition, similar to the one described by Hawking and Page, which occurs at a critical temperature determined by both the black hole mass and by the strength of the coupling.