Quasibound states of analytic black-hole configurations in three and four dimensions

TL;DR

This paper analytically investigates quasibound states in acoustic black-hole analogs in 2+1 and 3+1 dimensions, revealing effects of horizons and stability properties using hypergeometric functions.

Contribution

It provides an exact analytical method for quasibound states in acoustic black-hole models, enhancing understanding of horizon effects and stability in analog gravity systems.

Findings

Derived explicit quasibound state frequencies.

Analyzed stability of acoustic black-hole configurations.

Presented radial eigenfunctions for these states.

Abstract

In this work we analyze the sound perturbation of Unruh's acoustic effective geometry in both (2+1) and (3+1) spacetime dimensions and present an exact analytical expression for the quasibound states of these idealized black-hole configurations by using a new approach recently developed, which uses the polynomial conditions of the hypergeometric functions. Our main goal is to discuss the effects of having an event horizon in such effective metrics. We also discuss the stability of the systems and present the radial eigenfunctions related to these quasibound state frequencies. These metrics assume just the form it has for a Schwarzschild black hole near the event horizon, and therefore may, in principle, shed some light into the underlying classical and quantum physics of astrophysical black holes through analog acoustic probes.