Thermodynamics of de Sitter black holes: Thermal cosmological constant

We study the thermodynamic properties associated with the black hole event horizon and the cosmological horizon for black hole solutions in asymptotically de Sitter spacetimes. We examine thermodynamics of these horizons on the basis of the conserved charges according to Teitelboim’s method. In particular, we have succeeded in deriving the generalized Smarr formula among thermodynamical quantities in a simple and natural way. We then show that cosmological constant must decrease when one takes into account the quantum effect. These observations have been obtained if and only if the cosmological constant plays the role of a thermodynamical state variable. We also touch upon the relation between inflation of our universe and a phase transition of black holes.