Maxwell's equal area law for Vaidya-Bonner-de Sitter black hole under Lorentz invariance violation

Abstract

In this study, we investigate the tunneling of fermions with arbitrary spin near the event horizon of a nonstationary Vaidya-Bonner-de Sitter (VBdS) black hole under Lorentz invariance violation (LIV). The modified Hawking temperature of VBdS black holes is calculated by using tortoise coordinate transformation, Feynman prescription, and Wentzel–Kramers–Brillouin approximation. By considering the cosmological constant as a thermodynamic pressure in the extended phase space, we construct a Maxwell's equal area law under LIV and study the phase transitions of VBdS black hole in , , and planes. The LIV increases the length of the liquid-gas coexistence region. The thermodynamic quantities such as the entropy, heat capacity, Helmholtz free energy, internal energy, enthalpy, and Gibbs free energy of the VBdS black hole are discussed. These quantities tend to increase under LIV. The stability of the black hole is also discussed in the presence of LIV.