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Abstract

The first chapter is introductory.

The second chapter considers Einstien-Maxwell equations which admit a null Killing vector and a* null electromagnetic field. I present certain solutions of these Einstien-Maxwell equations. This work is based on earlier work described in Kramer et al 1980 and Boachie and Islam 1983.

In the next chapter, I calculate the expansion, shear and rotation of certain axially symmetric solutions found by Islam (1977, 1983). In Chapter 4, I find Killing vectors for the solution found by Islam (1983) mentioned earlier. I also apply to these Killing vectors the analysis applied by Bonnor (1980) to the Van Stockum solution (1937) to determine if there are any time-like hypersuperface-orthogonal Killing vectors, and show that Islam's solution is not static but stationary.

In Islam 1983, he found out exact global solution of Einstien-Maxwell equations. The solution thus obtained is regular and well behaved inside the matter. Such matched solutions are rare either for the Einstien or Einstien-Maxwell equations. Considering those solutions in Chapter 5, I have calculated out all nine curvature invariants. The invariants of the Riemann curvature tensor are first found in terms of its equivalent curvature invariants in terms of two-spinors given by Witten (1959) and Penros (1960). We consider briefly some properties of these invariants

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science > QA Mathematics
Departments:	School of Science & Technology > Department of Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

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