The Dynamical Instability of Rotating Boson Stars
We investigate the dynamical instability of rotating boson stars described by the Gross--Pitaevskii--Poisson equations with contact self-interactions. Through three-dimensional simulations, we confirm that the rotating boson star undergoes a quasiperiodic conversion between ring-like and twin-star-like density configurations in the early nonlinear stage. We develop a systematic linear stability analysis to identify the modes driving this instability and show that repulsive self-interactions could significantly increase the lifetime of the rotating boson stars. We further construct a three-mode Hamiltonian to describe the early nonlinear stage, which explains the quasiperiodic conversion. This analytical framework agrees reasonably well with the simulation results and provides a clear picture to understand the dynamics of rotating boson stars.