Energy and momentum distributions of a (2+1)-dimensional black hole background

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.