Collapse and Nonlinear Instability of AdS Space with Angular Momentum

We present a numerical study of rotational dynamics in AdS_{5} with equal angular momenta in the presence of a complex doublet scalar field. We determine that the endpoint of gravitational collapse is a Myers-Perry black hole for high energies and a hairy black hole for low energies. We investigate the time scale for collapse at low energies E, keeping the angular momenta J∝E in anti-de Sitter (AdS) length units. We find that the inclusion of angular momenta delays the collapse time, but retains a t∼1/E scaling. We perturb and evolve rotating boson stars, and find that boson stars near AdS space appear stable, but those sufficiently far from AdS space are unstable. We find that the dynamics of the boson star instability depend on the perturbation, resulting either in collapse to a Myers-Perry black hole, or development towards a stable oscillating solution.