Resonant frequencies of a massless scalar field in the canonical acoustic black hole spacetime

TL;DR

This paper derives exact solutions for a massless scalar field in a canonical acoustic black hole spacetime, using Heun functions, to analyze the resonant frequencies associated with this system.

Contribution

It provides the first exact analytical solutions for scalar fields in this specific acoustic black hole spacetime, revealing detailed resonance properties.

Findings

Exact solutions expressed in terms of Heun functions

Analysis of resonant frequencies in the acoustic black hole

Insights into wave behavior in analogue gravity systems

Abstract

In this work we consider the exact solution of the Klein-Gordon equation describing a massless scalar field in the spacetime of a four dimensional canonical acoustic black hole, which is given in terms of the general Heun function, to investigate the interesting phenomena related to the resonant frequencies.