Stability of branes trapped by d-dimensional black holes

TL;DR

This paper analyzes the stability of codimension-one branes positioned at the equator of various d-dimensional black holes, revealing stability in some cases and instability in others through analytical and numerical methods.

Contribution

It provides the first comprehensive stability analysis of branes in different black hole backgrounds, including Schwarzschild, Schwarzschild-(anti-)de Sitter, and Schwarzschild-de Sitter spacetimes.

Findings

Branes are stable in Schwarzschild and Schwarzschild-anti-de Sitter backgrounds.

Branes are unstable against s-wave perturbations in Schwarzschild-de Sitter background.

Analytical methods confirm stability in certain geometries, while numerics reveal instability in others.

Abstract

The system of extended objects interplaying with a black hole describes or mimics various gravitational phenomena. In this brief paper, we report the results of stability analysis of codimension-one Dirac-Nambu-Goto branes rest at the equatorial plane of $d$-dimensional spherical black holes, including the Schwarzschild and Schwarzschild-(anti-)de Sitter black holes. For the Schwarzschild and Schwarzschild-anti-de Sitter backgrounds the stability of branes is shown analytically by means of a deformation technique. In contrast, for the Schwarzschild-de Sitter background we demonstrate with the help of numerics that the brane is unstable (only) against the s-wave sector of perturbations.