Perturbations of a Stringy Black Hole

TL;DR

This paper extends a three-dimensional stringy black hole to four dimensions, analyzes its global properties, and investigates its stability under small perturbations, finding positive definite potentials indicating stability.

Contribution

It introduces a four-dimensional extension of the stringy black hole and analyzes its stability, which was not previously established.

Findings

Potential for axial perturbations is positive definite.

The extended black hole is stable under small perturbations.

Global properties of the four-dimensional solution are discussed.

Abstract

We extend the three dimensional stringy black hole of Horne and Horowitz to four dimensions. After a brief discussion of the global properties of the metric, we discuss the stability of the background with respect to small perturbations, following the methods of Gilbert and of Chandrasekhar. The potential for axial perturbations is found to be positive definite.