New class of LRS spacetimes with simultaneous rotation and spatial twist.
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Date
2016
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Abstract
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.
Description
Master of Science in Mathematics. University of KwaZulu-Natal, Durban 2016.