Generalised superradiant scattering

TL;DR

This paper establishes the precise conditions under which superradiance occurs, emphasizing the importance of boundary conditions and showing that ergoregions alone are insufficient, with implications for analogue gravity models.

Contribution

It provides a comprehensive framework for identifying superradiant systems based on necessary and sufficient conditions, clarifying misconceptions about ergoregions and superradiance.

Findings

Ergoregions alone do not guarantee superradiance.

Boundary conditions like ingoing waves at horizons are crucial.

Certain analogue models without horizons do not exhibit superradiance.

Abstract

We analyse the necessary and sufficient conditions for the occurrence of superradiance. Starting with a wave equation we examine the possibility of superradiance in terms of an effective potential and boundary conditions. In particular, we show that the existence of an ergoregion is not sufficient; an appropriate boundary condition, e.g. only ingoing group velocity waves at an event horizon, is also crucial. After applying our scheme to the standard examples of superradiance, we show that analogue models of gravity without an event horizon do not necessarily exhibit superradiance. Particularly, we show that the superradiant phenomenon is absent in purely rotating inviscid fluids with vorticity. We argue that there should be a catalogue of superradiant systems that can be found by focusing on the necessary and sufficient conditions outlined below.