Energy distribution in a BTZ black hole spacetime

TL;DR

This paper calculates the energy distribution of a (2+1)-dimensional rotating BTZ black hole using two different energy-momentum complexes, finding identical results that support their equivalence in three-dimensional gravity.

Contribution

It demonstrates that Landau-Lifshitz and Weinberg complexes yield the same energy distribution for the BTZ black hole, supporting their equivalence in 3D gravitational backgrounds.

Findings

Both complexes produce identical energy distributions.

Results support the equivalence of energy-momentum complexes in 3D.

Findings align with known results in 4D gravity.

Abstract

We evaluate the energy distribution associated with the (2+1)-dimensional rotating BTZ black hole. The energy-momentum complexes of Landau-Lifshitz and Weinberg are employed for this computation. Both prescriptions give exactly the same form of energy distribution. Therefore, these results provide evidence in support of the claim that, for a given gravitational background, different energy-momentum complexes can give identical results in three dimensions, as it is the case in four dimensions.