The Klein-Gordon Equation of a Rotating Charged Hairy Black Hole in (2+1) Dimensions

TL;DR

This study analyzes the behavior of a massive scalar field in a rotating charged hairy black hole background in (2+1) dimensions, revealing periodic solutions and boundary conditions for scalar fields near such black holes.

Contribution

It provides analytical and numerical solutions to the Klein-Gordon equation in a 3D charged rotating hairy black hole, including special cases and boundary condition analysis.

Findings

Scalar field exhibits periodic-like behavior near black holes.

Analytical solutions involve hypergeometric and Kummer functions.

Numerical solutions show periodicity and boundary conditions for scalar fields.

Abstract

In this paper, we consider the Klein-Gordon equation in a 3D charged rotating hairy black hole background to study behavior of a massive scalar field. In the general case we find periodic-like behavior for the scalar field which may be vanishes at the black hole horizon or far from the black hole horizon. For the special cases of non-rotating or near horizon approximation we find radial solution of Klein-Gordon equation in terms of hypergeometric and Kummer functions. Also for the case of uncharged black hole we find numerical solution of the Klein-Gordon equation as periodic function which may enhanced out of the black hole or vanish at horizon. We find allowed boundary conditions which yield to the identical bosons described by scalar field.