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.. 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.