Unstable Schwarzschild-Tangherlini black holes in fourth-order gravity

TL;DR

This paper investigates the stability of higher-dimensional Schwarzschild-Tangherlini black holes within fourth-order gravity, revealing that their Gregory-Laflamme instability stems from the massive nature of perturbations rather than ghost states.

Contribution

It demonstrates the presence of Gregory-Laflamme instability in Schwarzschild-Tangherlini black holes in fourth-order gravity, linking instability to massiveness of perturbations.

Findings

Unstable modes similar to Gregory-Laflamme instability are found.

Instability is caused by the massive nature of perturbations, not ghost states.

Stable in Einstein gravity but unstable in fourth-order gravity.

Abstract

We study the stability of Schwarzschild-Tangherlini (ST) black holes in fourth-order gravity which provides a higher dimensional linearized massive equation. The linearized-Ricci tensor perturbation is employed to exhibit unstable modes featuring the Gregory-Laflamme (GL) instability of higher dimensional black strings, in comparison to the stable ST black holes in Einstein gravity. It turns out that the GL instability of the ST black holes in the fourth-order gravity originates from the massiveness, but not a nature of fourth-order derivative theories giving ghost states.