On Black Hole Stability in Multidimensional Gravity

TL;DR

This paper investigates the stability of multidimensional black hole solutions in Einstein-Maxwell-scalar gravity, finding that solutions without a dilaton are stable, whereas those with naked singularities are unstable.

Contribution

It introduces a family of multidimensional dilatonic black-hole solutions and analyzes their stability under spherical perturbations, highlighting the stability of non-dilatonic solutions.

Findings

Non-dilatonic black holes are stable under perturbations.

Solutions with naked singularities are unstable.

The paper characterizes properties of solutions in higher-dimensional gravity.

Abstract

Exact static, spherically symmetric solutions to the Einstein-Maxwell-scalar equations, with a dilatonic-type scalar-vector coupling, in $D$-dimensional gravity with a chain of $n$ Ricci-flat internal spaces are considered. Their properties and special cases are discussed. A family of multidimensional dilatonic black-hole solutions is singled out, depending on two integration constants (related to black hole mass and charge) and three free parameters of the theory (the coordinate sphere, internal space dimensions, and the coupling constant). The behaviour of the solutions under small perturbations preserving spherical symmetry, is studied. It is shown that the black-hole solutions without a dilaton field are stable, while other solutions, possessing naked singularities, are catastrophically unstable.