Catastrophic Instability of Small Lovelock Black Holes

TL;DR

This paper investigates the stability of Lovelock black holes across different dimensions, revealing that small black holes are generally unstable under certain perturbations, leading to catastrophic instability.

Contribution

It demonstrates the dimension-dependent instability of small Lovelock black holes under tensor and scalar perturbations, extending understanding of their stability properties.

Findings

Lovelock black holes are stable under vector perturbations in all dimensions.

Small Lovelock black holes are unstable under tensor perturbations in even dimensions.

Small Lovelock black holes are unstable under scalar perturbations in odd dimensions.

Abstract

We study the stability of static black holes in Lovelock theory which is a natural higher dimensional generalization of Einstein theory. We show that Lovelock black holes are stable under vector perturbations in all dimensions. However, we prove that small Lovelock black holes are unstable under tensor perturbations in even-dimensions and under scalar perturbations in odd-dimensions. Therefore, we can conclude that small Lovelock black holes are unstable in any dimensions. The instability is stronger on small scales and hence catastrophic in the sense that there is no smooth descendant.