Quasinormal modes in Lorentz violating black hole analogues

Analogue models of black holes typically have collective excitations with a dispersion relation that breaks the effective Lorentz symmetry at high energy. We investigate the consequences of such Lorentz violations on the quasinormal modes (QNMs) of the system, that is, the modes of energy dissipation. The model involves low frequency capillary-gravity waves (whose dispersion relation can be adjusted between sub- and superluminal modifications) around a draining vortex, which mimics a rotating black hole spacetime. For a subluminal/superluminal modification, the frequency and decay rate of co-rotating modes can be reduced/increased substantially, whilst counter-rotating modes are barely affected. A further consequence of the superluminal modification is that there are no corotating QNMs above a critical rotation and no counter-rotating ones below a critical rotation for strong enough Lorentz violations.