Separability of Klein-Gordon equation on near horizon extremal Myers-Perry black hole

We investigate the separability of the Klein-Gordon equation on near horizon of d-dimensional rotating Myers-Perry black hole in two limits: (i) generic extremal case and (ii) 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 behavior in small- and large-r regions.

Automated summary

The separability of the Klein-Gordon equation near the horizon of a rotating Myers-Perry black hole in d dimensions is investigated in two limits: generic extremal case and extremal vanishing horizon case. The temperature of the black hole vanishes in the generic extremal case due to a relation between mass and rotation parameters, while in the extremal vanishing horizon case, one rotation parameter is restricted to zero on top of the extremality condition. The Klein-Gordon equation is shown to be separable in both cases, with the radial part of the equation being solved and its behavior discussed in small- and large-r regions.