### Abstract:

Energy-momentum is an important conserved quantity whose definition has been a focus of many investigations in general relativity. Unfortunately, there is still no generally accepted definition of energ3r and momentum in general relativity. Attempts aimed at finding a quantity for describing distribution of energy-momentum due to matter, non-gravitational and gravitational fields only resulted in various energy-momentum complexes (these are nontensorial under general coordinate transformations) whose physical meaning have been questioned. The problems associated with energy-momentum complexes re¬sulted in some researchers even abandoning the concept of energy-momentum localization in favor of the alternative concept of quasi-localization. However, quasi-local masses have their inadequacies, while the remarkable work of Virbhadra and some others, and recent results of Cooperstock and Chang et ai have revived an interest in various energy-momentum complexes. Hence in this work we use energy-momentum complexes to obtain the energy dis¬tributions in various space-times.
We elaborate on the problem of energy localization in general relativity and use energy-momentum prescriptions of Einstein, Landau and Lifshitz, Papapetrou, Weinberg, and Moller to investigate energy distributions in var¬ious space-times. It is shown that several of these energy-momentum com¬plexes give the same and acceptable results for a given space-time. This shows the importance of these energy-momentum complexes. Our results agree with Virbhadra's conclusion that the Einstein's energy-momentum complex is still the best tool for obtaining energy distribution in a given space-time. The Cooperstock hypothesis (that energy and momentum in a curved space-time are confined to the the regions of non-vanishing energy-momentum of matter and the non-gravitational field) is also supported.

### Description:

Thesis presented for the Degree of Doctor of Philosophy in Applied Mathematics, Department of Mathematical Sciences at the University of Zululand, 2002.