Notes on non-extremal, charged, rotating black holes in minimal D=5 gauged supergravity

We consider the non-extremal, charged, rotating black hole solution of five-dimensional minimal gauged supergravity of Cvetič, Lü and Pope [Phys. Lett. B 598 (2004) 273]. We compute the Ashtekar–Magnon–Das mass and show it agrees with the thermodynamic mass. We find a reducible Killing tensor and integrate the geodesic equation explicitly. We also compute the Euclidean action of the black hole and show it satisfies the quantum statistical relation. Further we present a Smarr relation. We end with a discussion of applications to string theory.