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

Understand

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.