General nonextremal rotating charged godel black holes in minimal five-dimensional gauged supergravity

I present the general exact solutions for nonextremal rotating charged black holes in the Godel 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 Godel 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-Godel black hole backgrounds.