Analytic solutions in the acoustic black hole analogue of the conical Kerr metric

TL;DR

This paper derives analytical solutions for sound perturbations in a rotating acoustic black hole with a disclination, providing explicit dependence on defect parameters and obtaining the exact Hawking-Unruh radiation spectrum.

Contribution

It presents the first analytical solutions of the Klein-Gordon equation in a rotating acoustic black hole with a disclination, linking defect parameters to the perturbation spectrum.

Findings

Analytical solutions expressed in Heun form for the perturbation equation.

Explicit dependence of solutions on disclination parameters.

Exact Hawking-Unruh radiation spectrum derived.

Abstract

We study the sound perturbation of a rotating acoustic black hole in the presence of a disclination. The radial part of the massless Klein-Gordon equation is written into a Heun form, and its analytical solution is obtained. These solutions have an explicit dependence on the parameter of the disclination. We obtain the exact Hawking-Unruh radiation spectrum.