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In this paper, the modified Hawking radiation and the P-v criticality ofReissner-Nordstr{\"o}m-de Sitter (RNdS) black hole are investigated by usingDirac equation with Lorentz violation theory in curved space time. Takingcosmological constant as the thermodynamic pressure and its conjugate quantityas thermodynamic volume, the analogy between the RNdS black hole in theensemble with fixed charge and van der Waals liquid-gas system is derived. Wealso study the equation of state, critical exponents, critical point, heatcapacity, entropy correction, Gibbs free energy. It is worth mentioning thatthe critical temperature, entropy, Gibbs free energy and Helmholtz free energyare modified but the critical exponents are found to be unchanged due to theinfluence of Lorentz violation theory. We observe that the number ofHawking-Page critical point increases due to Lorentz violation theory.

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