The black hole bomb and superradiant instabilities

TL;DR

This paper explores the superradiant instability of Kerr black holes when surrounded by a mirror, analyzing conditions for instability, calculating growth timescales, and discussing stability in Kerr-AdS black holes.

Contribution

It provides detailed analysis of the black hole bomb mechanism, including timescales, frequencies, and conditions for instability, and offers explicit examples and stability criteria.

Findings

A minimum mirror distance is required for instability.

The system's growth timescale depends on mirror placement.

Large Kerr-AdS black holes are stable, small ones are unstable.

Abstract

A wave impinging on a Kerr black hole can be amplified as it scatters off the hole if certain conditions are satisfied giving rise to superradiant scattering. By placing a mirror around the black hole one can make the system unstable. This is the black hole bomb of Press and Teukolsky. We investigate in detail this process and compute the growing timescales and oscillation frequencies as a function of the mirror's location. It is found that in order for the system black hole plus mirror to become unstable there is a minimum distance at which the mirror must be located. We also give an explicit example showing that such a bomb can be built. In addition, our arguments enable us to justify why large Kerr-AdS black holes are stable and small Kerr-AdS black holes should be unstable.