Explosion and final state of an unstable Reissner-Nordstrom black hole

TL;DR

This study uses numerical relativity to explore the nonlinear evolution of superradiant instabilities in charged black holes, revealing the formation of hairy black holes and explosive phenomena depending on scalar charge.

Contribution

First detailed numerical simulation of superradiant instability evolution in charged black holes leading to hairy black hole formation and explosive energy dynamics.

Findings

Final state is a hairy black hole with scalar condensate.

Energy extraction can overshoot, causing explosive phenomena.

Charge extraction does not reverse during evolution.

Abstract

A Reissner-Nordstr\"om black hole (BH) is superradiantly unstable against spherical perturbations of a charged scalar field, enclosed in a cavity, with frequency lower than a critical value. We use numerical relativity techniques to follow the development of this unstable system -- dubbed a charged BH bomb -- into the non-linear regime, solving the full Einstein--Maxwell--Klein-Gordon equations, in spherical symmetry. We show that: $i)$ the process stops before all the charge is extracted from the BH; $ii)$ the system settles down into a hairy BH: a charged horizon in equilibrium with a scalar field condensate, whose phase is oscillating at the (final) critical frequency. For low scalar field charge, $q$, the final state is approached smoothly and monotonically. For large $q$, however, the energy extraction overshoots and an explosive phenomenon, akin to a $bosenova$, pushes some energy back into the BH. The charge extraction, by contrast, does not reverse.