THERMODYNAMIC STUDY OF SPECIFIC BLACK HOLE INSPIRED BY GENERALIZED ENTROPY

         The term “black hole” is of a very recent origin. It was coined in 1969 by the American scientist John Wheeler, as a graphic description to an idea that dates to at least two hundred years, to a time when there were two theories about light-the corpuscular theory and the wave theory. We now have a more concise theory in this respect-the wave-particle duality theory of quantum mechanics. John Michell, in 1783, was the first to provide a breakthrough, through his paper, Philosophical transactions of the royal society of London. In this paper, he pointed out that a star that was sufficiently massive and compact will have such a strong gravitational field that even light cannot escape-any light emitted from the surface of the star will be dragged back by the star’s gravitational attraction before it could get very far. Michell suggested that there might be large number of stars just like this. Such entities which form black voids in space came to be known as black holes. Black hole thermodynamics is a rich subject, straddling both the classical and quantum aspects of gravity. The thermodynamic charges of a black hole such as entropy and temperature, while intrinsically quantum in nature, are related to classical attributes such as horizon area and surface gravity. Indeed, it was considering the classical response of a black hole to infalling matter that led Bardeen, Carter, and Hawking to make the link between black hole variations and laws of thermodynamics. More recently, our understanding of black hole thermodynamics and the interpretation of the various parameters has also been improving. The outline of this paper is as follows: First, we reviewed the various thermodynamic aspects of non-rotating and uncharged black holes like Reissner- Nordström, BTZ and Bardeen black holes. The findings were then incorporated to investigate, derive and compare thermodynamical parameters of Schwarzschild and Schwarzschild-AdS black holes. 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 behaviour 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 analysing 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.