Separability of Klein-Gordon Equation on Near Horizon Extremal Myers-Perry Black Hole

TL;DR

This paper demonstrates the separability of the Klein-Gordon equation on the near horizon of extremal Myers-Perry black holes in two specific limits, providing solutions for the radial part and analyzing its behavior.

Contribution

It shows that the Klein-Gordon equation is separable in both generic extremal and extremal vanishing horizon cases of Myers-Perry black holes, extending understanding of wave equations in these backgrounds.

Findings

Klein-Gordon equation is separable in both extremal cases.

Radial equation solutions are obtained and analyzed.

Behavior of solutions in small and large r regions is discussed.

Abstract

We investigate the separability of Klein-Gordon equation on near horizon of d-dimensional rotating Myers-Perry black hole in two limits : 1) generic extremal case and 2) extremal vanishing horizon case. In the first case , there is a relation between the mass and rotation parameters so that black hole temperature vanishes. In the latter case, one of the rotation parameters is restricted to zero on top of the extremality condition. We show that the Klein-Gordon equation is separable in both cases. Also, we solved the radial part of that equation and discuss its behaviour in small and large r regions.