Acoustic black holes: massless scalar field analytic solutions and analogue Hawking radiation

TL;DR

This paper derives analytic solutions for massless scalar fields in acoustic black hole spacetimes, exploring analogue Hawking radiation and spectral features of emitted scalar particles.

Contribution

It provides the first analytic solutions of the Klein-Gordon equation in acoustic black hole backgrounds using confluent Heun functions, advancing understanding of analogue Hawking radiation.

Findings

Analytic solutions expressed in confluent Heun functions

Characterization of scalar wave behavior near acoustic horizons

Discussion of spectral features of analogue Hawking radiation

Abstract

We obtain the analytic solutions of the radial part of the massless Klein-Gordon equation in the spacetime of both three dimensional rotating and four dimensional canonical acoustic black holes, which are given in terms of the confluent Heun functions. From these solutions, we obtain the scalar waves near the acoustic horizon. We discuss the analogue Hawking radiation of massless scalar particles and the features of the spectrum associated with the radiation emitted by these acoustic black holes.