A note on physical mass and the thermodynamics of AdS-Kerr black holes

Abstract

As with any black hole, asymptotically anti-de Sitter Kerr black holes are described by a small number of parameters, including a ``mass parameter'' M that reduces to the AdS-Schwarzschild mass in the limit of vanishing angular momentum. In sharp contrast to the asymptotically flat case, the horizon area of such a black hole increases with the angular momentum parameter a if one fixes M; this appears to mean that the Penrose process in this case would violate the Second Law of black hole thermodynamics. We show that the correct procedure is to fix not M but rather the ``physical'' mass E=M/(1−a2/L2)2; this is motivated by the First Law. For then the horizon area decreases with a. We recommend that E always be used as the mass in physical processes: for example, in attempts to ``over-spin'' AdS-Kerr black holes.