The Thermodynamical Behaviors of Kerr-Newman AdS Black Holes

We reconsider the study of critical behaviors of Kerr-Newman Anti-de Sitter(AdS)black holes in four dimensions.The study is made in terms of the moduli space parameterized by the charge Q and the rotation parameter a,relating the mass M of the black hole and its angular momentum J via the relation a=J/M.Specifically,we discuss such thermodynamical behaviors in the presence of a positive cosmological constant considered as a thermodynamic pressure and its conjugate quantity as a thermodynamic volume.The equation of state for a charged Reissner-Nordstrom AdS black hole predicts a critical universal number depending on the(Q,a)moduli space.In the vanishing limit of the a parameter,this prediction recovers the usual universal number in four dimensions.Then,we find the bounded region of the moduli space allowing the consistency of the model with real thermodynamical variables.