General Nonextremal Rotating Charged Gödel Black Holes in Minimal Five-Dimensional Gauged Supergravity

Abstract

I present the general exact solutions for nonextremal rotating charged black holes in the Gödel universe of five-dimensional minimal supergravity theory. They are uniquely characterized by four nontrivial parameters: namely, the mass m, the charge q, the Kerr equal rotation parameter a, and the Gödel parameter j. I calculate the conserved energy, angular momenta, and charge for the solutions and show that they completely satisfy the first law of black hole thermodynamics. I also study the symmetry and separability of the Hamilton-Jacobi and the massive Klein-Gordon equations in these Einstein-Maxwell-Chern-Simons-Gödel black hole backgrounds.

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.…”

Wave equation for the Wu black hole

“…We know from the original article [34] that the determinant of the metric can be written as 6) in our new coordinates and consequently we get…”

“…The goal of this paper is to study the separability of the massless scalar wave equation for a general stationary, axisymmetric metric with orthogonal transitivity and apply the results to the most general black hole solution in D=5 maximally supersymmetric gauged supergravity found by Wu [34]. While we derive the residua structure for a general stationary, axisymmetric metric with orthogonal transitivity, due to its complexity in D=5 with two angular momenta, three charges, and cosmological constant, Wu's solution is an excellent testing ground to study explicitly properties and structure of the wave equation; in particular the separability and the structure of the poles.…”

“…In [34], Wu's original solution of the general nonextremal rotating charged AdS black hole in five-dimensional U(1) 3 gauged supergravity is given as 12) to see the singularity structure better. Then the metric becomes…”