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Possibilities emerging out of the dynamical evolutions of collapsing systemsare addressed in this thesis through analytical investigations of the highlynon-linear Einstein Field Equations. Studies of exact solutions and theirproperties, play a non-trivial role in general relativity, even in the currentcontext. Finding non-trivial solutions to the Einstein field equations requiressome reduction of the problem, which usually is done by exploiting symmetriesor other properties. Exact solutions of the Einsteins field equationsdescribing an unhindered gravitational collapse are studied which generallypredict an ultimate singular end-state. In the vicinity of such a spacetimesingularity, the energy densities, spacetime curvatures, and all other physicalquantities blow up. Despite exhaustive attempts over decades, the famousconjecture that the formation of a singularity during stellar collapsenecessarily accompanies the formation of an event horizon, thereby covering thecentral singularity, still remains without a proof. Moreover, there areexamples of stellar collapse models with reasonable matter contribution inwhich an event horizon does not form at all, giving rise to a naked singularityfrom which both matter and radiation can fall in and come out. These examplessuggest that the so-called cosmic censorship conjecture may not be a generalrule. Therefore one must embark upon analysis of realistic theoretical modelsof gravitational collapse and gradually generalizing previous efforts.

Aspects of Gravitational Collapse and the formation of Spacetime Singularities