Stability of Lovelock Black Holes under Tensor Perturbations

TL;DR

This paper investigates the stability of static Lovelock black holes under tensor perturbations, revealing dimension-dependent stability properties and potential instabilities for small black holes, which are relevant for high-energy physics experiments.

Contribution

It derives a master equation for tensor perturbations in third order Lovelock theory and analyzes stability in seven and eight dimensions, identifying conditions for stability and instability.

Findings

Black holes are stable in seven dimensions within the linear regime.

In eight dimensions, black holes below a critical mass are unstable.

Small black holes are conjectured to be unstable in any dimension.

Abstract

We study the stability of static black holes in the third order Lovelock theory. We derive a master equation for tensor perturbations. Using the master equation, we analyze the stability of Lovelock black holes mainly in seven and eight dimensions. We find there are cases where the linear analysis breaks down. If we restrict ourselves to the regime where the linear analysis is legitimate, black holes are always stable in seven dimensions. However, in eight dimensions, there exists a critical mass below which black holes are unstable. Combining our result in the third order Lovelock theory with the previous one in Einstein-Gauss-Bonnet theory, we conjecture that small black holes are unstable in any dimensions. The instability found in this paper will be important for the analysis of black holes at the LHC.