First Law for Kerr Taub-NUT AdS Black Holes

The first law of black hole mechanics, which relates the change of energy to the change of entropy and other conserved charges, has been the main motivation for probing the thermodynamic properties of black holes. In this talk, we will investigate the thermodynamics of Kerr Taub-NUT AdS black holes. Employing two diffreent methods (Komar integrals and Brown-York charges) we show that our expressions for the black hole charges satisfy a Smarr formula. Further, we will establish the first law for the Kerr Taub-NUT AdS black holes. We indicate the relevance of these results to the entropy of rotating AdS black holes as one quarter of the event horizon area.