Properties of Rindler Horizon and Some Aspects of Black Hole Chemistry in Massive Gravity

Abstract

One 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.