The main objective of this thesis is to consider the concept ofgravitational entropy from a perturbative point of view. A flat,matter dominated universe model is subjected to a linear perturbation,and the entropic properties of the resulting universe areinvestigated.
We confirm that the classical thermodynamic entropy of such auniverse decreases with time as the perturbation grows, whichappears to be a breach of the second law of thermodynamics (SLT).According to the "Weyl Curvature Hypothesis", this can berectified by adding an extra term to the entropy called thegravitational entropy. This term arises from the geometry ofspace-time and takes into account the attractive nature of thegravitational force. The sum of the classical thermodynamic and thegravitational entropy defines a general entropy. It is this generalentropy quantity, and not the classical entropy alone, that mustsatisfy the SLT.
We consider a special type of localized density perturbations of a Gaussian form, and show that the total entropy does indeed increase. However, this requires a certain fine tuning of a dimensional constant which appears in the expression for the gravitational entropy.