  Possibilities emerging out of the dynamical evolutions of collapsing systems
are addressed in this thesis through analytical investigations of the highly
non-linear Einstein Field Equations. Studies of exact solutions and their
properties, play a non-trivial role in general relativity, even in the current
context. Finding non-trivial solutions to the Einstein field equations requires
some reduction of the problem, which usually is done by exploiting symmetries
or other properties. Exact solutions of the Einsteins field equations
describing an unhindered gravitational collapse are studied which generally
predict an ultimate singular end-state. In the vicinity of such a spacetime
singularity, the energy densities, spacetime curvatures, and all other physical
quantities blow up. Despite exhaustive attempts over decades, the famous
conjecture that the formation of a singularity during stellar collapse
necessarily accompanies the formation of an event horizon, thereby covering the
central singularity, still remains without a proof. Moreover, there are
examples of stellar collapse models with reasonable matter contribution in
which an event horizon does not form at all, giving rise to a naked singularity
from which both matter and radiation can fall in and come out. These examples
suggest that the so-called cosmic censorship conjecture may not be a general
rule. Therefore one must embark upon analysis of realistic theoretical models
of gravitational collapse and gradually generalizing previous efforts.

General Relativity and Quantum Cosmology