Thermodynamic study of specific black hole inspired by generalized entropy

Abstract

This study examines the thermodynamic features of the Van der Waals black hole within the context of three parameters of entropy. It is discovered that the parameters of black hole, including mass and temperature, deviate from those that are derived with the Boltzmann-Gibbs paradigm. Furthermore, the entropy parameter influences the behavior of the Gibbs free energy by introducing thermodynamic instabilities, whereas the emission rate is mostly affected by entropy parameters at low frequencies. We provide expressions for thermodynamic quantities like pressure, temperature, heat capacity, Gibbs free energy, Helmholtz free energy, and isothermal compressibility. We investigate the phase structure of these solutions by analyzing their heat capacity and Gibbs free energy. This investigation also examines the critical behavior and phase transitions of black hole. Additionally, we observe both local and global stability of black hole in the canonical ensemble for a variety of parameter values. We also investigate the effect of the entropy parameter and the sparsity of Hawking radiation on black hole evaporation.