Energy-Momentum Localization for a Space-Time Geometry Exterior to a Black Hole in the Brane World

TL;DR

This paper examines the energy-momentum distribution outside a black hole in brane world models using coordinate-dependent complexes, revealing dependence on radial distance, black hole mass, and a specific parameter, with momenta being zero.

Contribution

It applies Landau-Lifshitz and Weinberg prescriptions to a brane world black hole metric, showing how energy depends on parameters and recovering Schwarzschild geometry for a special case.

Findings

Energy depends on radial coordinate, black hole mass, and a parameter.

All momenta are zero in the studied prescriptions.

Schwarzschild space-time is recovered for a specific parameter value.

Abstract

In general relativity one of the most fundamental issues consists in defining a generally acceptable definition for the energy-momentum density. As a consequence, many coordinate-dependent definitions have been presented, whereby some of them utilize appropriate energy-momentum complexes. We investigate the energy-momentum distribution for a metric exterior to a spherically symmetric black hole in the brane world by applying the Landau-Lifshitz and Weinberg prescriptions. In both the aforesaid prescriptions, the energy thus obtained depends on the radial coordinate, the mass of the black hole and a parameter $\lambda_{0}$, while all the momenta are found to be zero. It is shown that for a special value of the parameter $\lambda_{0}$, the Schwarzschild space-time geometry is recovered. Some particular and limiting cases are also discussed.