Superradiance and Instability of Black Holes
Hideo Kodama
TL;DR
This work investigates the stability of rotating black holes in higher dimensions, focusing on Kerr–AdS spacetimes and the interplay between superradiant scattering and gravitational instabilities. It derives a general scalar-field superradiance condition in asymptotically flat spacetimes and then analyzes AdS–Kerr backgrounds where the reflective AdS boundary can trap energy, potentially triggering a black-hole–bomb-like instability. Remarkably, for simply rotating AdS–Kerr black holes, tensor-type gravitational perturbations map to a scalar-field problem, yielding a stability bound $\ell^2 a^2 \le r_h^4$ and predicting instability for $\ell^2 a^2 > r_h^4$; this links rotational dynamics, boundary conditions, and gravitational stability. The results emphasize the role of a globally timelike Killing vector (Hawking–Reall) and motivate numerical studies to quantify growth rates and explore the $\Lambda \to 0$ limit in higher-dimensional contexts.
Abstract
We discuss the relation between the superradiance phenomenon and the instability of rotating black holes in higher dimensions. In particular, we point out that the superradiant instability of a massless scalar field around a simply rotating Kerr-adS black hole implies the gravitational instability of that black hole for tensor-type perturbations.