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

TL;DR

This paper explores the thermodynamics and phase transitions of Vaidya-Bonner-de Sitter black holes under Lorentz invariance violation, revealing LIV's effects on thermodynamic stability and coexistence regions.

Contribution

It introduces a novel analysis of Maxwell's equal-area law and phase transitions for VBdS black holes considering LIV effects, extending thermodynamic studies to non-stationary black holes.

Findings

LIV extends the liquid-gas coexistence region.

Thermodynamic quantities increase under LIV.

Black hole stability is influenced by LIV effects.

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, Feynman 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.