On the thermodynamic aspects of gravity

Abstract: Here the Weyl curvature hypothesis is examined using the gravitational entropy (GE). We have considered the family of C-metric accelerating black holes and evaluated their corresponding gravitational entropy. Then we studied the GE in some isotropic and anisotropic cosmologies utilizing the definition proposed by Clifton, Ellis, and Tavakol, where the Bel-Robinson tensor is used to determine the energy-momentum tensor of the free gravitational field. We checked whether, in the vicinity of the initial cosmic singularity, the ratio of the energy density of free gravity to that of matter density goes to zero or not. We showed that whenever this is true, the gravitational entropy increases monotonically with the structure formation of the universe and discussed the conditions of validity for the Weyl curvature hypothesis. Subsequently, the next part of the thesis deals with the validity of two different proposals of gravitational entropy (GE) in traversable wormhole systems. We found that the GE proposals do provide us with a consistent measure of GE in several wormhole solutions. In the later portion of the thesis, we examined the validity of the generalized second law of thermodynamics (GSLT) in an expanding FRW universe filled with different variants of the Chaplygin gas. Lastly, we studied the evolution of the FRW universe in the presence of variable modified Chaplygin gas and obtained its temperature and other parameters as a function of the redshift. Finally, the thesis is concluded.