Abstract
The main objective of this thesis is to consider the concept of
gravitational 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 are
investigated.
We confirm that the classical thermodynamic entropy of such a
universe decreases with time as the perturbation grows, which
appears to be a breach of the second law of thermodynamics (SLT).
According to the "Weyl Curvature Hypothesis", this can be
rectified by adding an extra term to the entropy called the
gravitational entropy. This term arises from the geometry of
space-time and takes into account the attractive nature of the
gravitational force. The sum of the classical thermodynamic and the
gravitational entropy defines a general entropy. It is this general
entropy quantity, and not the classical entropy alone, that must
satisfy 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.