Wave equation for the Wu black hole
Abstract
Wu black hole is the most general solution of maximally supersymmetric gauged supergravity in D=5, containing U(1)^{3} gauge symmetry. We study the separability of the massless KleinGordon equation and probe its singularities for a general stationary, axisymmetric metric with orthogonal transitivity, and apply the results to the Wu black hole solution. We start with the zero azimuthalangle eigenvalues in the scalar field Ansatz and find that the residuum of a pole in the radial equation is associated with the surface gravity calculated at this horizon. We then generalize our calculations to nonzero azimuthal eigenvalues and probing each horizon singularity, we show that the residua of the singularities for each horizon are in general associated with a specific combination of the surface gravity and the angular velocities at the associated horizon. It turns out that for the Wu black hole both the radial and angular equations are general Heun's equations with four regular singularities.
 Publication:

Journal of High Energy Physics
 Pub Date:
 September 2014
 DOI:
 10.1007/JHEP09(2014)121
 arXiv:
 arXiv:1407.8173
 Bibcode:
 2014JHEP...09..121B
 Keywords:

 Black Holes in String Theory;
 Supergravity Models;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology;
 Mathematical Physics
 EPrint:
 19 pages, minor corrections and reference added. Matches the published version