A study of the holonomy group of space-time is undertaken and related to the Segre and Petrov types of then Weyl and <I>E</I>-tensors respectively. Attention is then focused on the <I>E</I>-tensor, and a theorem is proved which states that any space-time <I>M</I> can be disjointly decomposed into open sets on which the Segre type of the <I>E</I>-tensor is constant, the union of which if dense in <I>M. </I>This theorem is then applied to prove a similar theorem for the Ricci tensor using the principal null directions of the <I>E</I>-tensor. Finally, a study of proper projective symmetry in null and non-null Einstein-Maxwell and static, spherically symmetric space-times is performed. A theorem is proved which states that no proper projective symmetry is possible in any null Einstein-Maxwell space-times. This result is then extended to the non-null case under some general restrictions. The static, spherically symmetric space-times are then considered, and those admitting proper projective symmetry are completely determined. The proper projective vector fields are also explicitly calculated.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:369628 |
| Date | January 2001 |
| Creators | Khan, Muhsan A. |
| Publisher | University of Aberdeen |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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