Superradiant instabilities of rotating black holes in the time domain

• Published in: arXiv.org
• Main Author: Dolan, Sam R
• Format: Paper Journal Article
• Language: English
• Published: Ithaca Cornell University Library, arXiv.org 01.07.2013
• Subjects: Boson fields; Boundary conditions; Couplings; Fourier analysis; Growth rate; Perfectly matched layers; Physics - General Relativity and Quantum Cosmology; Physics - High Energy Astrophysical Phenomena; Physics - High Energy Physics - Theory; Rotation; Spacetime; Stability analysis; Time domain analysis
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1212.1477

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 \(t \lesssim 5 \times 10^6 M\), 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 \(\tau^{-1} \approx 1.72 \times 10^{-7} (GM/c^3)^{-1}\) for the massive scalar field on Kerr spacetime.