Semi-tetrad decomposition of spacetime with conformal symmetry.
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Date
2018
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Abstract
In this thesis, we study the kinematical and dynamical properties of a general spacetime
that admits a conformal Killing vector. A 1+1+2 decomposition of the spacetime
is performed using the fluid 4-velocity and a preferred spatial direction in the 3-space.
The Lie derivatives of the 4-velocity vector and the preferred spatial direction vector
are calculated and analyzed. We compare our results with the 1+3 decomposition
of Maartens et al (1986), and find new results in the form of a scalar equation and
constraint equation owing to the further decomposition. This provides new insights
into the behaviour of the acceleration, expansion, shear and vorticity scalars which
are not possible in the 1+3 decomposition. The general energy momentum tensor
for an anisotropic fluid is considered and decomposed using the semi-tetrad covariant
approach. We take the Lie derivative along the conformal Killing vector and apply
to Einstein’s field equations. This makes it possible to generate a set of constraint
equations in the new geometrical variables. All the geometrical and thermodynamical
quantities are written in terms of the 1+1+2 decomposition variables. This is a new
result. We also find a system of equations that must be satisfied by the thermodynamical
variables when a conformal symmetry exists applied to the perfect fluid case. We
show that the conformal factor satisfies a damped wave equation with a potential.
Description
Master’s degree. University of KwaZulu-Natal, Durban.