Scalar field conformally coupled to a charged BTZ black hole

TL;DR

This paper investigates the behavior of a conformally coupled scalar field in a charged BTZ black hole background, solving the Klein-Gordon equation using special functions, and explores the effects of non-linear Maxwell fields.

Contribution

It provides an analytical solution to the Klein-Gordon equation in a charged BTZ black hole with a conformal Maxwell field, highlighting the role of special functions in the solution.

Findings

Radial solutions involve Heun functions in general

Pure gravity limit yields hypergeometric solutions

Coupling to non-linear Maxwell field influences scalar field behavior

Abstract

We study the Klein-Gordon equation of a scalar field conformally coupled to a charged BTZ black hole. The background metric is obtained by coupling a non-linear and conformal invariant Maxwell field to (2+1) gravity. We show that the radial part is generally solved by a Heun function and, in the pure gravity limit, by a hypergeometric function.