# Pure Lovelock black hole in the dimension, $d=3N+1$, is stable

## TL;DR

This paper demonstrates the stability of pure Lovelock black holes in specific higher dimensions and compares their quasinormal modes to Einstein black holes, revealing dimension-dependent oscillation frequencies.

## Contribution

It establishes the stability of pure Lovelock black holes in dimensions $d=3N+1$, extending previous instability results for Gauss-Bonnet black holes, and analyzes their quasinormal mode spectra.

## Key findings

- Pure Lovelock black holes in $d=3N+1$ are stable.
- Perturbation decay times are weakly dependent on dimension.
- Quasinormal mode frequencies depend on the dimension.

## Abstract

In this paper we show that pure Lovelock static Schwarzschild's analogue black hole in dimensions $d>3N+1$, where $N$ is the degree of Lovelock polynomial action, is stable even though pure Gauss-Bonnet $N=2$ black hole is unstable in dimension $d<7$. We also discuss and compare quasinormal modes for pure Lovelock and the corresponding Einstein black hole in the same dimension. We find that perturbations decay with characteristic time which is weakly dimensional dependent as it depends only on the gravitational potential of the background solution, while frequency of oscillations however depend on the dimension. Also we show that spectrum of perturbations is not isospectral except in $d=4$.