2. Thesis and Dissertations
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Item Properties of Rindler Horizon and Some Aspects of Black Hole Chemistry in Massive Gravity(National Institute Of Technology Karnataka Surathkal, 2023) T K, Safir; Vaid, DeepakOne of the biggest challenges in theoretical physics, beyond any doubt, is the lack of a successful theory that describes how gravity works quantum mechanically. Ex- ploring black holes provides many promising pathways that might lead us to a positive solution for the problem at hand. One of the tools in this regard is the thermodynamic behavior of black holes. To this extent, this thesis deals with certain aspects of black hole thermodynamics. First, we probe the microstructure of the dRGT massive black hole in an anti-de Sitter background. The calculations are performed in an extended phase space with pressure and volume taken as fluctuation variables. We analyze the microstructure by exploiting the Ruppeiner geometry, where the thermodynamic cur- vature scalar is constructed via adiabatic compressibility. The nature of the curvature scalar along the coexistence line of small (SBH) and large (LBH) black holes is inves- tigated. In the microscopic interaction, we observe that the SBH phase behaves as an anyonic gas and the LBH phase is analogous to a boson gas. Further, we study the effect of graviton mass on the underlying microstructure of the black hole. The thermodynamic study in the massive gravity theory can be extended further by considering the dynamics of phase transition. The dynamical properties of the stable small-large black hole phase transitions in dRGT non-linear massive gravity theory are studied based on the underlying free energy landscape. The free energy landscape is constructed by specifying the Gibbs free energy to every state, and the free energy profile is used to study the different black hole phases. The small-large black hole states are characterized by a probability distribution function, and the kinetics of phase transition is described by the Fokker-Planck equation. Further, a detailed study of the first passage process is presented, which describes the dynamics of phase transition. We have investigated the effect of mass and topology on the dynamical properties of phase transitions of black holes in dRGT massive gravity theory. Finally, we concentrate on the characteristics and features of the first law of black hole thermodynamics. The physical process version of the first law can be obtained for bifurcate-Killing horizons with certain assumptions. Especially, one has to restrict to the situations where the horizon evolution is quasi-stationary, under perturbations.We revisit the analysis of this assumption considering the horizon perturbations of the Rindler horizon by a spherically symmetric object. We demonstrate that even if the quasi-stationary assumption holds, the change in entropy in four-dimensional space- time dimensions diverges when considered between asymptotic cross-sections. How- ever, these divergences do not appear in higher dimensions. We also analyze these fea- tures in the presence of a positive cosmological constant. In the process, we prescribe a recipe to establish the physical process first law in such ill-behaved scenarios.Item Extended Phase Space Thermodynamics of Regular Bardeen Black Hole(National Institute Of Technology Karnataka Surathkal, 2023) K V, Rajani; Vaid, DeepakThe 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 ).