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

• Main Authors: Cvetic, M, Pope, C. N, Whiting, B. F, Zhang, Haoyu
• Format: Journal Article
• Language: English
• Published: 04-07-2022
• Subjects: Physics - General Relativity and Quantum Cosmology; Physics - High Energy Physics - Theory
• DOI: 10.48550/arxiv.2207.01653

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.