Gravitational Perturbations of Higher Dimensional Rotating Black Holes: Tensor Perturbations

TL;DR

This paper investigates gravitational perturbations of higher-dimensional rotating black holes, finding stability in flat space but superradiant instability in anti-de Sitter space, with potential endpoint being a nonaxisymmetric black hole.

Contribution

It provides a detailed analysis of tensor perturbations of Myers-Perry black holes with equal angular momenta in odd dimensions, including the effects of a cosmological constant.

Findings

No instability in asymptotically flat case.

Superradiant instability in asymptotically anti-de Sitter case.

Potential endpoint is a stationary, nonaxisymmetric black hole.

Abstract

Assessing the stability of higher-dimensional rotating black holes requires a study of linearized gravitational perturbations around such backgrounds. We study perturbations of Myers-Perry black holes with equal angular momenta in an odd number of dimensions (greater than five), allowing for a cosmological constant. We find a class of perturbations for which the equations of motion reduce to a single radial equation. In the asymptotically flat case we find no evidence of any instability. In the asymptotically anti-de Sitter case, we demonstrate the existence of a superradiant instability that sets in precisely when the angular velocity of the black hole exceeds the speed of light from the point of view of the conformal boundary. We suggest that the endpoint of the instability may be a stationary, nonaxisymmetric black hole.