The Klein–Gordon equation of a rotating charged hairy black hole in (2 + 1) dimensions

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 vanish 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 enhance out of the black hole or vanish at horizon. We find allowed boundary conditions which may yield to the identical bosons described by scalar field.