Analogue black string in a quantum harmonic oscillator

TL;DR

This paper derives exact solutions to the Klein-Gordon equation in a black string background using biconfluent Heun functions, exploring negative mass scenarios and quantum analogs to understand quasinormal modes.

Contribution

It provides the first exact solutions for scalar particles in a black string background and introduces a quantum system that mimics this environment.

Findings

Exact solutions involve biconfluent Heun functions.

Negative mass values lead to complex energy eigenvalues.

Quantum analog system replicates black string particle dynamics.

Abstract

For a scalar particle without self-interaction or backreaction from the space-time background, the dynamics are governed by the Klein-Gordon equation. In this work, we write the exact solution of this equation in the background of a chargeless, static black string in terms of the biconfluent Heun function. In this curious system, we are able to explore what happens if we have negative values for the masses. The eigenvalue problem provides complex energy values for the particle, which may indicate the presence of quasinormal modes. We show a simple quantum system that can imitate the particle in the black string background, whose solutions are also applications of the biconfluent Heun function.