paper

Superradiant instabilities of rotating black holes in the time domain

arXiv:1212.1477 · doi:10.1103/PhysRevD.87.124026

Abstract

Bosonic fields on rotating black hole spacetimes are subject to amplification by superradiance, which induces exponentially-growing instabilities (the `black hole bomb') in two scenarios: if the black hole is enclosed by a mirror, or if the bosonic field has rest mass. Here we present a time-domain study of the scalar field on Kerr spacetime which probes ultra-long timescales up to , to reveal the growth of the instability. We describe an highly-efficient method for evolving the field, based on a spectral decomposition into a coupled set of 1+1D equations, and an absorbing boundary condition inspired by the `perfectly-matched layers' paradigm. First, we examine the mirror case to study how the instability timescale and mode structure depend on mirror radius. Next, we examine the massive-field, whose rich spectrum (revealed through Fourier analysis) generates `beating' effects which disguise the instability. We show that the instability is clearly revealed by tracking the stress-energy of the field in the exterior spacetime. We calculate the growth rate for a range of mass couplings, by applying a frequency-filer to isolate individual modal contributions to the time-domain signal. Our results are in accord with previous frequency-domain studies which put the maximum growth rate at for the massive scalar field on Kerr spacetime.

17 pages, 13 figures, to match journal version

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