Superradiance in dispersive black hole analogues

TL;DR

This paper develops a framework to analyze mode interactions in dispersive wave equations and applies it to black hole analogues, revealing how dispersion influences superradiant scattering and amplification.

Contribution

It introduces a new method based on classical turning points to analyze mode interactions in dispersive systems and applies it to black hole analogues with novel insights.

Findings

Superradiant amplification range is modified by dispersion.

Additional modes can reflect superradiant modes, complicating amplification observation.

Reflection coefficients are estimated in the dispersive regime.

Abstract

Wave equations containing spatial derivatives which are higher than second order arise naturally in the context of condensed matter systems. The solutions of such equations contain more than two modes and consequently, the range of possible interactions between the different modes is significantly enhanced compared to the two mode case. We develop a framework for analysing the different mode interactions based on the classical turning points of the dispersion relation. We then apply this framework to the scattering of deep water gravity waves with a draining bathtub vortex, a system which constitutes the analogue of a rotating black hole in the non-dispersive limit. In particular, we show that the different scattering outcomes are controlled by the light-ring frequencies, a concept routinely applied in black hole physics, and two new frequencies which are related to the strength of dispersion. We find that the frequency range in which the reflected wave is superradiantly amplified appears as a simple modification to the non-dispersive case. However, the condition to observe this amplification is complicated by the fact that a superradiant mode can be reflected back into the system by scattering with one of the additional modes. We provide estimates for the reflection coefficients in the full dispersive regime.