6533b821fe1ef96bd127ad76

RESEARCH PRODUCT

Dynamical formation of a Reissner-Nordström black hole with scalar hair in a cavity

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In a recent Letter [Sanchis-Gual et al., Phys. Rev. Lett. 116, 141101 (2016)], 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 nonlinear regime, until it relaxed into an equilibrium configuration, found to be a 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. In particular, we find sufficiently large self-interactions suppress the exponential growth phase, known from linear theory, and promote a nonmonotonic behavior of the scalar field energy. Furthermore, we discuss in detail the influence of the various parameters in this model: the initial BH charge, the initial scalar perturbation, the scalar field charge, the mass, and the position of the cavity's boundary (mirror). We also investigate the ``explosive'' nonlinear regime previously reported to be akin to a bosenova. A mode analysis shows that the ``explosions'' can be interpreted as the decay into the BH of modes that exit the superradiant regime.