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.

An analysis of the wave equation for the U (1) 2 gauged supergravity black hole

“…The analysis confirms the analogous anticipated structure obtained [22] for the most general black holes in five-dimensional maximally supersymmetric gauge supergravity [21]. The analysis of the radial part of the wave equation therefore carries the key information about the internal structure of the black hole, associated with all the horizons.…”

“…This feature of the wave equation was explicitly demonstrated [18,19] for the general black hole in minimal five-dimensional gauged supergravity with three equal charges [20]. Most recently, the study of the massless Klein-Gordon equation for the most general black hole solution of five-dimensional maximally supersymmetric gauged supergravity with U(1) 3 gauge symmetry [21] was presented in [22]. In spite of the complexity of the metric, the separability of wave equation was demonstrated and the radial part was cast in a form with the poles of the horizon equation, whose residua were again written in the specific form containing the associated surface gravities and angular velocities.…”

AdS5 black hole entropy near the BPS limit

“…The general AdS 5 black hole solution (for any M , Q I , J i ) is known [12] but has not been analyzed in much detail [43]. In this section we follow most of the literature and focus on diagonal R-charges Q 1 = Q 2 = Q 3 .…”

Killing horizons: Negative temperatures and entropy super-additivity

“…The Wu black hole [85] is 5D, three charge rotating solution with negative cosmological constant (∝ g 2 ). Employing expressions from [86] for a product of the entropy and temperature of this black hole, associated with all three horizons we obtain the following interesting expression:…”