Instability of Small Lovelock Black Holes in Even-dimensions

TL;DR

This paper investigates the stability of static black holes in Lovelock theory across various dimensions, deriving a master equation for tensor perturbations and revealing that small black holes in even dimensions are unstable.

Contribution

It derives a general master equation for tensor perturbations in Lovelock black holes, simplifying stability analysis to an algebraic problem and identifying instability in small even-dimensional black holes.

Findings

Small Lovelock black holes in even dimensions are unstable.

The stability problem reduces to an algebraic condition based on a single functional.

A general master equation for tensor perturbations in Lovelock theory is derived.

Abstract

We study the stability of static black holes in Lovelock theory which is a natural higher dimensional generalization of Einstein theory. We derive a master equation for tensor perturbations in general Lovelock theory. It turns out that the resultant equation is characterized by one functional which determines the background black hole solutions. Thus, the stability issue of static black holes under tensor perturbations in general dimensions is reduced to an algebraic problem. We show that small Lovelock black holes in even-dimensions are unstable.