Dynamic and thermodynamic stability and negative modes in Schwarzschild-anti-de Sitter black holes

The thermodynamic properties of Schwarzschild-anti-de Sitter black holes confined within finite isothermal cavities are examined. In contrast with the Schwarzschild case. the infinite cavity limit may he taken which, if suitably stated, remains double valued. This allows the correspondence between the nonexistence of negative modes for classical solutions and local thermodynamic stability of the equilibrium configuration of such solutions to be shown in a well defined manner. This is not possible in the asymptotically flat case. Furthermore. the nonexistence of negative modes for the larger black hole solution in the Schwarzschild-anti-de Sitter case provides strong evidence in favor of the recent positive energy conjecture of Horowitz and Myers.