Abstract
Abstract In this paper, we investigate the tunneling of fermions with arbitrary spin near the event horizon of non-stationary Vaidya-Bonner-de Sitter black hole (VBdS) in Lorentz invariance violation (LIV). The modified Hawking temperature of VBdS black holes is calculated by using tortoise coordinate transformation, Fenyman prescription and WKB approximation. By considering cosmological constant as a thermodynamic pressure in the extended phase space, we construct Maxwell's equal-area law in LIV and study the phase transitions of VBdS black hole in $P-v$, $P-V$ and $T-S$ plane. The LIV increases the length of liquid-gas coexistence region. The thermodynamic quantities such as entropy, heat capacity, Helmholtz free energy, Internal energy, enthalpy and Gibbs free energy of VBdS black hole are discussed. These quantities tend to increase under LIV. The stability of black hole is also discussed in the presence of LIV.
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