Journal
INTERNATIONAL JOURNAL OF MODERN PHYSICS A
Volume 18, Issue 32, Pages 5949-5963Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0217751X03016823
Keywords
general relativity; black holes
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Using Einstein, Landau-Lifshitz, Papapetrou and Weinberg energy-momentum complexes, we explicitly evaluate the energy and momentum distributions associated with a nonstatic and circularly symmetric three-dimensional space-time. The gravitational background under study is an exact solution of Einstein's equations in the presence of a cosmological constant and a null fluid. It can be regarded as the three-dimensional analogue of the Vaidya metric and represents a nonstatic spinless (2 + 1)-dimensional black hole with an outflux of null radiation. All four above-mentioned prescriptions give exactly the same energy and momentum distributions for the specific black hole background. Therefore, the results obtained here provide evidence in support of the claim that for a given gravitational background, different energy-momentum complexes can give identical results in three dimensions. Furthermore, in the limit of zero cosmological constant, the results presented here reproduce those obtained by Virbhadra. He utilized the Landau-Lifshitz energy-momentum complex for the same (2 + 1)-dimensional black hole background in the absence of a cosmological constant.
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