The study of exact solutions to the Einstein and Einstein-Maxwell field equations,
by imposing a symmetry requirement on the manifold, has been the subject of much
recent research. In this thesis we consider specifically conformal symmetries in static
and nonstatic spherically symmetric spacetimes. We find conformally invariant solutions,
for spherically symmetric vectors, to the Einstein-Maxwell field equations
for static spacetimes. These solutions generalise results found previously and have
the advantage of being regular in the interior of the sphere. The general solution to
the conformal Killing vector equation for static spherically symmetric spacetimes is
found. This solution is subject to integrability conditions that place restrictions on
the metric functions. From the general solution we regain the special cases of Killing
vectors, homothetic vectors and spherically symmetric vectors with a static conformal
factor. Inheriting conformal vectors in static spacetimes are also identified. We
find a new class of accelerating, expanding and shearing cosmological solutions in
nonstatic spherically symmetric spacetimes. These solutions satisfy an equation of
state which is a generalisation of the stiff equation of state. We also show that this
solution admits a conformal Killing vector which is explicitly obtained. / Thesis (Ph.D.)-University of Natal, Durban, 1993.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:ukzn/oai:http://researchspace.ukzn.ac.za:10413/8004 |
| Date | January 1993 |
| Creators | Maharaj, M. S. |
| Contributors | Maharaj, Sunil D., Maartens, R. |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
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