Rotating Black Holes in Gauged Supergravities; Thermodynamics, Supersymmetric Limits, Topological Solitons and Time Machines

We study the thermodynamics of the recently-discovered non-extremal charged rotating black holes of gauged supergravities in five, seven and four dimensions, obtaining energies, angular momenta and charges that are consistent with the first law of thermodynamics. We obtain their supersymmetric limits by using these expressions together with an analysis of the AdS superalgebras including R-charges. We give a general discussion of the global structure of such solutions, and apply it in the various cases. We obtain new regular supersymmetric black holes in seven and four dimensions, as well as reproducing known examples in five and four dimensions. We also obtain new supersymmetric non-singular topological solitons in five and seven dimensions. The rest of the supersymmetric solutions either have naked singularities or naked time machines. The latter can be rendered non-singular if the asymptotic time is periodic. This leads to a new type of quantum consistency condition, which we call a Josephson quantisation condition. Finally, we discuss some aspects of rotating black holes in Godel universe backgrounds.