Instability of Charged Lovelock Black Holes: Vector Perturbations and Scalar Perturbations

TL;DR

This paper investigates the stability of charged Lovelock black holes under vector and scalar perturbations, establishing stability criteria and identifying conditions for instability, especially in small charge black holes.

Contribution

It introduces a new stability analysis framework using symmetric Schrödinger-type equations for charged Lovelock black holes, and identifies instability conditions for small charge cases.

Findings

Black holes are stable under vector perturbations.

Scalar perturbations can cause instability in small charge black holes.

Nearly extremal black holes are unstable under tensor perturbations.

Abstract

We examine the stability of charged Lovelock black hole solutions under vector type and scalar type perturbations. We find the suitable master variables for the stability analysis; the equations for these variables are the Schrodinger type equations with two components and these Schrodinger operators are symmetric. By these master equations, we show that charged Lovelock Black holes are stable under vector type perturbations. For scalar type perturbations, we show the criteria for the instability and check these numerically. In our previous paper, we have shown that nearly extremal black holes have the instability under tensor type perturbations. In this paper, we find that black holes with small charge have the instability under scalar type perturbations even if they have relatively large mass.