Instability of hairy black holes in regularized 4-dimensional Einstein-Gauss-Bonnet gravity

TL;DR

This paper investigates the existence and linear stability of hairy black holes in a regularized 4D Einstein-Gauss-Bonnet gravity, finding they are universally unstable with associated strong coupling issues.

Contribution

It demonstrates that asymptotically-flat hairy black holes in this theory are linearly unstable and identifies a strong coupling problem in the perturbation analysis.

Findings

Hairy black holes are unstable against linear perturbations.

Instability occurs for all values of the rescaled Gauss-Bonnet coupling.

A strong coupling problem affects the kinetic term of perturbations.

Abstract

In regularized 4-dimensional Einstein-Gauss-Bonnet (EGB) gravity derived from a Kaluza-Klein reduction of higher-dimensional EGB theory, we study the existence and stability of black hole (BH) solutions on a static and spherically symmetric background. We show that asymptotically-flat hairy BH solutions realized for a spatially-flat maximally symmetric internal space are unstable against linear perturbations for any rescaled GB coupling constant. This instability is present for the angular propagation of even-parity perturbations both in the vicinity of an event horizon and at spatial infinity. There is also a strong coupling problem associated with the kinetic term of even-parity perturbations vanishing everywhere.