New class of LRS spacetimes with simultaneous rotation and spatial twist.
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In this thesis we study Locally Rotationally Symmetric (LRS) spacetimes in which there exists a unique preferred spatial direction at each point. The conventional 1+3 decomposition of spacetime is extended to a 1+1+2 decomposition which is a natural setting in LRS models. We establish the existence and find the necessary and sufficient conditions for a new class of solutions of LRS spacetimes that have non-vanishing rotation and spatial twist simultaneously. In this study there are three key questions. By relaxing the condition of a perfect fluid, that is by introducing pressure anisotropy and heat flux, is it possible to have dynamical solutions with non-zero rotation and non-zero twist? If yes, can these solutions be physical? What are the local geometrical properties of such solutions? We investigate these questions in detail by using the semi-tetrad 1+1+2 covariant formalism. It is transparently shown that the existence of such solutions demand non-vanishing and bounded heat flux and these solutions are self-similar. We provide a brief algorithm indicating how to solve the system of field equations with the given Cauchy data on an initial spacelike Cauchy surface. We indicate that these solutions can be used as a first approximation from spherical symmetry to study rotating, inhomogeneous, dynamic and radiating astrophysical stars.