Ergoregion instabilities in rotating two-dimensional Bose--Einstein condensates: new perspectives on the stability of quantized vortices

We investigate the stability of vortices in two-dimensional Bose--Einstein condensates. In analogy with rotating spacetimes and with a careful account of boundary conditions, we show that the dynamical instability of multiply quantized vortices in trapped condensates persists in untrapped, spatially homogeneous geometries and has an ergoregion nature with some modification due to the peculiar dispersion of Bogoliubov sound. Our results open new perspectives to the physics of vortices in trapped condensates, where multiply quantized vortices can be stabilized by interference effects and singly charged vortices can become unstable in suitably designed trap potentials. We show how superradiant scattering can be observed also in the short-time dynamics of dynamically unstable systems, providing an alternative point of view on dynamical (in)stability phenomena in spatially finite systems.