Instability of Black Holes with a Gauss-Bonnet Term

TL;DR

This paper studies the fragmentation instability of hairy black holes with a Gauss-Bonnet term, revealing that some perturbatively stable black holes can become unstable through fragmentation, depending on coupling parameters.

Contribution

It introduces a non-perturbative analysis of black hole fragmentation instability in Gauss-Bonnet gravity with dilaton hair, providing phase diagrams and stability conditions.

Findings

Perturbatively stable black holes can be unstable under fragmentation.

Fragmentation instability depends on the Gauss-Bonnet coupling and black hole mass.

Phase diagrams illustrate stability regions for black holes.

Abstract

We investigate the fragmentation instability of hairy black holes in the theory with a Gauss$-$Bonnet(GB) term in asymptotically flat spacetime. Our approach is through the non-perturbative fragmentation instability. By this approach, we investigate whether the initial black hole can be broken into two black holes by comparing the entropy of the initial black hole with the sum of those of two fragmented black holes. The relation between the black hole instability and the GB coupling with dilaton hair are presented. We describe the phase diagrams with respect to the mass of the black hole solutions and coupling constants. We find that a perturbatively stable black hole can be unstable under fragmentation.