Stability of Generalised Static Black Holes in Higher Dimensions

TL;DR

This paper investigates the stability of higher-dimensional static black holes, demonstrating stability for Schwarzschild types using S-deformation and identifying potential instabilities against scalar perturbations in certain charged or neutral cases.

Contribution

The authors develop gauge-invariant master equations for black hole perturbations and apply S-deformation techniques to prove stability in higher dimensions.

Findings

Schwarzschild black holes are stable under perturbations.

Potential instability exists against scalar perturbations in some charged or neutral cases.

The S-deformation method effectively proves stability in higher-dimensional black holes.

Abstract

We discuss the stability of (charged) static black holes in higher-dimensional spacetimes with and without cosmological constant by using gauge-invariant master equations of the Schroedinger equation type for black hole perturbations derived by the authors recently. In particular, we show that the stability of higher-dimensional Schwarzschild black holes can be proved with the help of a technique called S-deformation of the master equations. We also point out that higher-dimensional static black holes might be unstable only against scalar-type perturbations in the neutral case and in the charged case with spherically symmetric or flat horizons.