  Using Einstein, Landau-Lifshitz, Papapetrou and Weinberg energy-momentum
complexes we explicitly evaluate the energy and momentum distributions
associated with a non-static and circularly symmetric three-dimensional
spacetime. The gravitational background under study is an exact solution of the
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 non-static 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 the
results obtained by Virbhadra who utilized the Landau-Lifshitz energy-momentum
complex for the same (2+1)-dimensional black hole background in the absence of
a cosmological constant.
