Extended Phase Space Thermodynamics of Regular Bardeen Black Hole

Abstract

The existence of black holes were predicted by Einstein’s general relativity, a remarkable theory that agrees with most observations at the solar system scale and beyond. However, in general relativity, black holes have singularities at their centers, as Hawking and Penrose’s famous theorems claimed. Regular black hole models, for example, have been offered as a way to get around the central singularity. Regular black holes have a de Sitter core at their center, which generates outward radial pressure to prevent gravitational collapse and the formation of singularities. The exact nature of astrophysical black holes, however, is unknown. As a result, it is critical to deduce deformations to the classical Schwarzschild metric using regular black hole models as motivation and to confirm astrophysical observations in a more generic and relevant framework. This thesis investigates the thermodynamic phase transition of regular Bardeen AdS black holes with and without quintessence surrounded by it. The cosmological constant Λ is given the status of thermodynamic variable pressure because of the in- consistency between the Smarr relation and the first law of black hole thermodynamics in AdS spacetime. The first law of black hole thermodynamics has been modified to include a pressure-volume term. Black hole phase behavior is found to be analogous to everyday physical phenomena in this extended phase space. The thermodynamics of the black hole is analyzed in extended phase space. A first-order phase transition analogous to the van der Waals system is evident from this study, which is affirmed by the specific heat divergence at the critical points. A conventional heat engine is constructed by considering the black hole as a working substance. The efficiency is obtained via a thermodynamic cycle in the P − v plane, which receives and ejects heat. The heat engine efficiency in regular Bardeen AdS black holes is improved by adding a quintessence field. The analytical expression for heat engine efficiency is derived in terms of the quintessence dark energy parameter. The study of Joule Thomson (JT) expansion in the regular Bardeen AdS black holes in the quintessence background is based on the analysis of inversion temperature and isenthalpic curves. The derivation of the JT coefficient µ is used to plot the inversion and isenthalpic curves. The effect ofquintessence parameters a and ωq on the JT coefficient and inversion temperature, es- pecially with the case of ωq = −1, −2/3 and −1/3 shows that quintessence dark energy affects the inversion point (Ti , Pi ).