Topological Black Holes with curvature induced scalarization in the extended scalar-tensor theories

TL;DR

This paper investigates the stability and phase transitions of topological black holes within extended scalar-tensor-Gauss-Bonnet gravity, revealing a transition to hairy black hole configurations for small sizes through analytical and numerical methods.

Contribution

It introduces a detailed analysis of scalar perturbations and quasi-normal modes in topological black holes with curvature-induced scalarization in extended scalar-tensor theories.

Findings

Identification of a phase transition to hairy black holes for small black holes.

Calculation of quasi-normal modes for scalar perturbations.

Evidence of curvature-induced scalarization in extended scalar-tensor theories.

Abstract

We study the perturbative behaviour of topological black holes in the presence of a cosmological constant and a scalar field coupled to the Gauss-Bonnet term. We calculate both analytically and numerically the quasi-normal modes of scalar perturbations in the extended scalar-tensor-Gauss-Bonnet gravity. In the case of small black holes we find a phase transition of the topological black hole to a hairy configuration.