Classical instability in Lovelock gravity

TL;DR

This paper presents a straightforward method to analyze the classical stability of static black hole solutions in Lovelock gravity, especially for high angular momentum modes, without needing explicit solutions.

Contribution

It introduces a new, simple approach for stability analysis in Lovelock gravity applicable even when explicit solutions are unknown.

Findings

Method correctly identifies unstable modes in known solutions.

Applicable to high angular momentum instabilities.

Does not require explicit black hole solutions.

Abstract

We introduce a simple method for the investigation of the classical stability of static solutions with a horizon in Lovelock gravity. The method is applicable to the investigation of high angular momentum instabilities, similar to those found by Dotti and Gleiser for Gauss-Bonnet black holes. The method does not require the knowledge of the explicit analytic form of the black hole solution. In this paper we apply our method to a case where the explicit solution is known and show that it identifies correctly the resulting unstable modes.