Fatal Effects of Charges on Stability of Black Holes in Lovelock Theory

TL;DR

This paper investigates how electric charges influence the stability of higher-dimensional black holes in Lovelock theory, revealing that small charged black holes near extremal mass are unstable, indicating charges can destabilize these black holes.

Contribution

It derives stability criteria for charged black holes in Lovelock theory and demonstrates that charges can induce instability, extending previous neutral black hole stability results.

Findings

Small charged black holes near extremal mass are unstable.

Neutral black holes in odd dimensions are stable.

Charges have destabilizing effects on black holes in Lovelock theory.

Abstract

We study the stability of static spherically symmetric charged black holes under tensor type perturbations in Lovelock theory which is a natural higher dimensional generalization of Einstein theory. We derive the master equation for tensor type perturbations and present the criterions for the stability. Examining these criterions numerically, we show that a black hole with small charge has the instability if its mass is as small as extreme mass. Combined with our previous result that neutral black hole has no dynamical instability in odd dimensions, this result suggests that charges have fatal effects on black holes in Lovelock theory.