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

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 $d=4$.

arXiv comment7 pages, 4 figures, v2 accepted for publication in PRD, conclusions unchanged

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• Galactic Pure Lovelock Blackholes: Geometry, stability, and Hawking temperature
• Strong cosmic censorship conjecture for a charged BTZ black hole
• Pure Gauss-Bonnet NUT Black Hole Solution: I
• Connecting quasi-normal modes with causality in Lovelock theories of gravity
• Tidal deformation of black holes in Lovelock gravity
• Absence of curvature singularities in symmetric perfect fluid spacetimes in Einstein-Gauss-Bonnet Gravity
• Pure Gauss-Bonnet NUT Black Hole Solution: II
• Lower bound of black hole hair in pure Lovelock theory of gravity