Hairy black resonators and the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>AdS</mml:mi></mml:mrow><mml:mrow><mml:mn>4</mml:mn></mml:mrow></mml:msub></mml:mrow></mml:math> superradiant instability
Paul M. Chesler
Abstract
The superradiant instability of Kerr-anti--de Sitter black holes is studied by numerically solving the full $3+1$ dimensional Einstein equations. We find that the superradiant instability results in a two stage process with distinct initial and secondary instabilities. At the end of the secondary instability the geometry oscillates at several distinct fundamental frequencies---a multioscillating black hole. The multioscillating black hole is remarkably close to a black resonator, albeit with a bit of gravitational hair. During the hairy black resonator epoch, the evolution of the horizon area is consistent with the exponential approach to a constant. By employing different seed perturbations in the initial Kerr-anti--de Sitter geometry, we also demonstrate that the black resonator's hair is not unique. In the dual quantum field theory description, rotation invariance is spontaneously broken and the energy density is negative in some regions, signaling an exotic state of matter which does not relax to a stationary configuration.