The energy-momentum problem in general relativity
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Date
2002
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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.
Keywords
General relativity (Physics), Mathematics, Mathematical physics