Dynamical formation of a Reissner-Nordstr\"om black hole with scalar hair in a cavity

Understand

In a recent letter, we presented numerical relativity simulations, solving the full Einstein--Maxwell--Klein-Gordon equations, of superradiantly unstable Reissner-Nordstr\"om black holes (BHs), enclosed in a cavity.

• Low frequency, spherical perturbations of a charged scalar field, trigger this instability.
• The system's evolution was followed into the non-linear regime, until it relaxed into an equilibrium configuration, found to be a $\textit{hairy}$ BH: a charged horizon in equilibrium with a scalar field condensate, whose phase is oscillating at the (final) critical frequency.
• Here, we investigate the impact of adding self-interactions to the scalar field.