Analytical investigation of wave absorption by a rotating black hole analogue

TL;DR

This paper analytically studies wave absorption in a rotating black hole analogue using confluent Heun functions, providing results that closely match numerical simulations, thereby enhancing understanding of wave behavior in analogue gravity models.

Contribution

It introduces an analytical approach to wave absorption in a draining vortex analogue of a rotating black hole using confluent Heun functions, validated by numerical comparison.

Findings

Analytical expressions for wave absorption length obtained.

Excellent agreement between analytical and numerical results.

Enhanced understanding of wave dynamics in analogue black hole models.

Abstract

Perturbations in a draining vortex can be described analytically in terms of confluent Heun functions. In the context of analogue models of gravity in ideal fluids, we investigate analytically the absorption length of waves in a draining bathtub, a rotating black hole analogue, using confluent Heun functions. We compare our analytical results with the corresponding numerical ones, obtaining excellent agreement.