# Collapse and Nonlinear Instability of AdS with Angular Momenta

## TL;DR

This study numerically explores the nonlinear stability and collapse dynamics of rotating scalar fields in AdS$_5$, revealing how angular momentum influences collapse times and stability of boson stars, and identifying endpoints as black holes.

## Contribution

It provides new insights into how angular momentum affects collapse times and stability of boson stars in AdS, including the delay of collapse and the nature of instability outcomes.

## Key findings

- Angular momentum delays gravitational collapse in AdS.
- Boson stars near AdS are stable, far from AdS are unstable.
- Collapse endpoints include Myers-Perry and hairy black holes.

## Abstract

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 timescale for collapse at low energies $E$, keeping the angular momenta $J\propto E$ in AdS length units. We find that the inclusion of angular momenta delays the collapse time, but retains a $t\sim1/E$ scaling. We perturb and evolve rotating boson stars, and find that boson stars near AdS appear stable, but those sufficiently far from AdS 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.