Rotating black holes in a draining bathtub: superradiant scattering of gravity waves

TL;DR

This paper models superradiant scattering of gravity waves in a rotating draining fluid, demonstrating wave amplification in a realistic setup with variable water depth, potentially observable experimentally.

Contribution

It introduces a new fluid flow model accounting for water depth variation and analyzes superradiance in this more realistic black hole analogue system.

Findings

Gravity waves are amplified via superradiance in the model.

Numerical results indicate experimental observation is feasible.

The system depends on two key dimensionless parameters.

Abstract

In a draining rotating fluid flow background, surface perturbations behave as a scalar field on a rotating effective black hole spacetime. We propose a new model for the background flow which takes into account the varying depth of the water. Numerical integration of the associated Klein-Gordon equation using accessible experimental parameters shows that gravity waves in an appropriate frequency range are amplified through the mechanism of superradiance. Our numerical results suggest that the observation of this phenomenon in a common fluid mechanical system is within experimental reach. Unlike the case of wave scattering around Kerr black holes, which depends only on one dimensionless background parameter (the ratio $a/M$ between the specific angular momentum and the mass of the black hole), our system depends on two dimensionless background parameters, namely the normalized angular velocity and surface gravity at the effective black hole horizon.