Abstract:
In this thesis we have investigated some solutions of Einstein's field equations having cylindrical symmetry. The corresponding energy momentum tensor of most of these solutions has pure radiation equation of state. First, the static Levi-Civita solution has been generalized to a Kasner type time dependent solution. Using this solution, we have presented a time dependent Vaidya type solution representing pure and gravitational radiation emitted from a nonstatic cylindrical source. As an application, we have analyzed a radiating nonstatic cosmic string like object. Next, we have presented cylindrically symmetric, static solutions of the Einstein field equations around a line singularity such that the energy momentum tensor corresponds to infinitely thin photonic shells composed of counter propagating pure radiation in certain directions. Positivity of the energy density of the thin shell and the line singularity is discussed. Among these solutions, a particular solution corresponding to a photonic shell whose interior and exterior is flat is interesting since the cylinder becomes a plane for an outside observer. We have also investigated the generalization of these solutions to multiple thin shells and found that line singularities including cosmic strings may be screened by photonic shells until they all appear as a planar wall. Lastly we have investigated solutions corresponding to circulating or counter circulating pure radiation around the axis. The first solution we have studied was an approximate thin shell solution corresponding to counter rotating photons with small contribution from an anisotropic fluid. Next, we study a cylindrical circulating beam of light. The gravitational field of a counter rotating pure radiation field is presented as a last solution for this thesis. These solutions can smoothly match to the corresponding vacuum solutions from either interior or exterior.
