Energy-Momentum Distribution of the Weyl-Lewis-Papapetrou and the Levi-Civita Metrics

TL;DR

This paper calculates energy-momentum distributions for Weyl-Lewis-Papapetrou and Levi-Civita metrics using various prescriptions, revealing differences that support a specific theoretical proposal.

Contribution

It provides a comparative analysis of energy-momentum densities for two exact Einstein solutions using multiple prescriptions, highlighting their differences.

Findings

Levi-Civita metric yields constant momentum with different energy densities.

Weyl-Lewis-Papapetrou metric shows prescription-dependent quantities.

Differences support Cooperstock's proposal regarding energy localization.

Abstract

This paper is devoted to compute the energy-momentum densities for two exact solutions of the Einstein field equations by using the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and M\"{o}ller. The spacetimes under consideration are the Weyl-Lewis-Papapetrou and the Levi-Civita metrics. The Weyl metric becomes the special case of the Weyl-Lewis-Papapetrou solution. The Levi-Civita metric provides constant momentum in each prescription with different energy density. The Weyl-Lewis-Papapetrou metric yields all the quantities different in each prescription. These differences support the well-defined proposal developed by Cooperstock and from the energy-momentum tensor itself.