Energy-Momentum Distribution: Some Examples

TL;DR

This paper examines energy-momentum distributions in various solutions of Einstein's equations using multiple prescriptions, revealing consistency in some cases and discrepancies in others, thus highlighting the complexity of energy localization in General Relativity.

Contribution

It compares different energy-momentum prescriptions across several exact solutions, providing insights into their consistency and limitations in energy-momentum localization.

Findings

Consistent energy-momentum results for Ferrari-Ibanez and Wainwright-Marshman solutions.

Inconsistent results for gravitational waves and Senovilla-Vera dust solutions.

Highlights the dependence of energy-momentum calculations on the chosen prescription.

Abstract

In this paper, we elaborate the problem of energy-momentum in General Relativity with the help of some well-known solutions. In this connection, we use the prescriptions of Einstein, Landau-Lifshitz, Papapetrou and M\"{o}ller to compute the energy-momentum densities for four exact solutions of the Einstein field equations. We take the gravitational waves, special class of Ferrari-Ibanez degenerate solution, Senovilla-Vera dust solution and Wainwright-Marshman solution. It turns out that these prescriptions do provide consistent results for special class of Ferrari-Ibanez degenerate solution and Wainwright-Marshman solution but inconsistent results for gravitational waves and Senovilla-Vera dust solution.