ENERGY AND MOMENTUM DISTRIBUTIONS OF A (2+1)-DIMENSIONAL BLACK HOLE BACKGROUND

Abstract

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.