## Investigation of gravitational collapse of generalized Vaidya spacetimes.

##### Abstract

In this thesis, we study the gravitational collapse of generalized Vaidya spacetimes
which describe a combination of lightlike and timelike matter elds, commonly known
as Type I and Type II elds, respectively, in the context of the cosmic censorship conjecture.
This conjecture suggests that singularities forming in gravitational collapse
should always be covered by event horizons of gravity. Many studies have been made
to establish this conjecture in a rigorous mathematical framework but it still remains
an open problem. We develop a general mathematical framework to study the conditions
on the mass function of generalized Vaidya spacetimes so that future directed
nonspacelike geodesics can terminate at the singularity in the past. Our result generalizes
earlier works on gravitational collapse. There exist classes of generalized Vaidya
mass functions for which the collapse terminates with a locally naked central singularity.
We calculate the strength of these singularities, to show that they are strong
curvature singularities, and there can be no extension of spacetime through them. We
then extend this analysis to higher dimensions and present su cient conditions on the
generalized Vaidya mass functions that will generate a locally naked singular end state.
With speci c examples, we show the existence of classes of mass functions that lead
to a naked singularity in four dimensions, which gets covered on transition to higher
dimensions. Hence for these classes of mass functions, cosmic censorship gets restored
in higher dimensions, and the transition to higher dimensions restricts the set of initial
data that results in a naked singularity.