Effects of nonlinear interactions on the superradiant instability of charged black holes

A Reissner-Nordström black hole (RNBH) enclosed in a cavity is known to be superradiantly unstable to charged scalar perturbations below a critical frequency. Inspired by the emergence of the QCD axion as a prominent dark matter candidate, we construct a model featuring an axion field coupled to an electromagnetic field that undergoes superradiant growth around an RNBH. Utilizing numerical relativity, we achieve stable, long-term evolution of this system and perform a comparative analysis across various parameter spaces. Our comprehensive investigation reveals the formation of a hairy black hole, whose final state is governed by a diverse set of physical parameters. Notably, the decay constant in the axion potential, representing nonlinear interactions, bifurcates the superradiant instability into two distinct behavioral regimes, leading to more significant dynamical shifts than previously reported. Furthermore, we examine the influence of the scalar field's charge and mass, as well as the mirror's position. We investigate the axionic bosenova process and observe a long-term beating pattern of the axion field induced by nonlinear interactions. By fine-tuning these parameter combinations, we demonstrate that the system can evolve toward a variety of distinct physical endpoints.