Mode Stability For Massless Scalars In Five-Dimensional Black Hole Backgrounds

TL;DR

This paper proves the mode stability of massless scalar fields in five-dimensional black hole backgrounds by extending techniques used in four-dimensional Kerr black holes, involving a transformation to an auxiliary spacetime without an ergoregion.

Contribution

It generalizes the mode stability proof from four-dimensional Kerr black holes to five-dimensional black hole solutions in Einstein gravity and supergravity.

Findings

Mode stability of massless scalar fields in five-dimensional black holes established.

Wave equation mapped to an ergoregion-free auxiliary spacetime.

Proof extends stability analysis to higher-dimensional black hole backgrounds.

Abstract

The mode stability of the Kerr black hole in four dimensions was demonstrated by Whiting in 1989, by separating the Teukolsky equation that describes gravitational perturbations and then transforming the radial and angular equations in such a way that the problem can be reformulated as a wave equation in an auxiliary spacetime in which the proof of stability is greatly simplified, owing to the absence of an ergoregion. As a preliminary step towards extending these ideas to higher-dimensional black holes, we study the mode stability of the massless scalar wave equation in the five-dimensional black hole solutions of Einstein gravity and supergravity. We show how the wave equation can again be mapped into one in an auxiliary spacetime in which there is no ergoregion, allowing us to give a proof of the mode stability of the solutions of the scalar wave equation.