Algebraically special resonances of the Kerr-black-hole-mirror bomb

TL;DR

This paper analytically investigates the resonant instabilities of higher-spin fields in the Kerr-black-hole-mirror system, revealing that electromagnetic and gravitational fields produce significantly more explosive superradiant instabilities than scalar fields.

Contribution

It extends the analysis of black-hole-mirror bombs to higher-spin fields and derives an analytic expression for the unstable resonance frequencies in rapidly rotating black holes.

Findings

Higher-spin black-hole bombs exhibit much larger instability growth rates than scalar bombs.

The resonance frequency is characterized by a specific relation involving black hole and field parameters.

Higher-spin fields lead to more explosive superradiant instabilities.

Abstract

A co-rotating bosonic field interacting with a spinning Kerr black hole can extract rotational energy and angular momentum from the hole. This intriguing phenomenon is known as superradiant scattering. As pointed out by Press and Teukolsky, the black-hole-field system can be made unstable (explosive) by placing a reflecting mirror around the black hole which prevents the extracted energy from escaping to infinity. This composed black-hole-mirror-field bomb has been studied extensively by many researchers. It is worth noting, however, that most former studies of the black-hole bomb phenomenon have focused on the specific case of confined scalar (spin-$0$) fields. In the present study we explore the physical properties of the higher-spin (electromagnetic and gravitational) black-hole bombs. It is shown that this composed system is amenable to an analytic treatment in the physically interesting regime of rapidly-rotating black holes. In particular, we prove that the composed black-hole-mirror-field bomb is characterized by the unstable resonance frequency $\omega=m\Omega_{\text{H}}+is\cdot 2\pi T_{\text{BH}}$ (here $s$ and $m$ are respectively the spin-parameter and the azimuthal harmonic index of the field, and $\Omega_{\text{H}}$ and $T_{\text{BH}}$ are respectively the angular-velocity and the temperature of the rapidly-spinning black hole). Our results provide evidence that the higher-spin (electromagnetic and gravitational) black-hole-mirror bombs are much more explosive than the extensively studied scalar black-hole-mirror bomb. In particular, it is shown here that the instability growth rates which characterize the higher-spin black-hole bombs are two orders of magnitudes larger than the instability growth rate of the scalar black-hole bomb.