P-v criticality of charged Reissner-Nordstr{\"o}m-de Sitter black hole under the influence of Lorentz violation theory

In this paper, the modified Hawking radiation and the P-v criticality of Reissner-Nordstr{\"o}m-de Sitter (RNdS) black hole are investigated by using Dirac equation with Lorentz violation theory in curved space time. Taking cosmological constant as the thermodynamic pressure and its conjugate quantity as thermodynamic volume, the analogy between the RNdS black hole in the ensemble with fixed charge and van der Waals liquid-gas system is derived. We also study the equation of state, critical exponents, critical point, heat capacity, entropy correction, Gibbs free energy. It is worth mentioning that the critical temperature, entropy, Gibbs free energy and Helmholtz free energy are modified but the critical exponents are found to be unchanged due to the influence of Lorentz violation theory. We observe that the number of Hawking-Page critical point increases due to Lorentz violation theory.