Hyperboloidal evolution of the Einstein equations applied to black hole superradiance of a charged scalar field

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Written by Olaf Baake

We study the superradiant behavior of a complex scalar field coupled to the Einstein-Maxwell equations. We write the system in an ADM-like formulation on constant mean curvature slices. The equations are derived in a conformally rescaled spacetime before spherical symmetry is imposed. We show that these equations are regular at infinity and solve them numerically in the massless case. The solutions we produce show superradiant as well as non-superradiant behavior.