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 Klein-Gordon 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 azimuthal-angle 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.

19 pages, minor corrections and reference added. Matches the published version

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• Universal Area Product Formulae for Rotating and Charged Black Holes in Four and Higher Dimensions
• Greybody Factors and Charges in Kerr/CFT
• Non-Extremal Rotating Black Holes in Five-Dimensional Gauged Supergravity
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Cited by in corpus (2)

• An Analysis of the Wave Equation for the $U(1{)}^2$ Gauged Supergravity Black Hole
• Hidden symmetries of black holes in five-dimensional supergravity