Thermodynamical aspect of charged rotating black holes in anti-de Sitter space

Thermodynamical properties of Kerr-Newman black holes are described in anti -de Sitter space. Typical thermodynamic functions are derived in geometrica l parameters. The black-hole solution is shown to exist at any finite tempe rature and to satisfy the so-called Bekenstein-Hawking relation. Local stab ility as well as the phase structure of the black-hole system is then exami ned for the canonical ensemble. Global stability of the black-hole system i s also discussed in proper reference to the value of angular velocity.