Teleparallel Energy-Momentum Distribution of Lewis-Papapetrou Spacetimes

TL;DR

This paper calculates the energy-momentum distribution of Lewis-Papapetrou spacetimes, a class of stationary axisymmetric solutions, using teleparallel theory and Möller prescription, revealing non-vanishing energy density and constant momentum components.

Contribution

It extends teleparallel energy-momentum analysis to Lewis-Papapetrou spacetimes, generalizing previous results for Weyl metrics with new insights into their energy-momentum characteristics.

Findings

Energy density is non-vanishing and well-defined.

Momentum components are constant except along the θ-direction.

Results reduce to Weyl metrics when ω=0.

Abstract

In this paper, we find the energy-momentum distribution of stationary axisymmetric spacetimes in the context of teleparallel theory by using M$\ddot{o}$ller prescription. The metric under consideration is the generalization of the Weyl metrics called the Lewis-Papapetrou metric. The class of stationary axisymmetric solutions of the Einstein field equations has been studied by Galtsov to include the gravitational effect of an {\it external} source. Such spacetimes are also astrophysically important as they describe the exterior of a body in equilibrium. The energy density turns out to be non-vanishing and well-defined and the momentum becomes constant except along $\theta$-direction. It is interesting to mention that the results reduce to the already available results for the Weyl metrics when we take $\omega=0$.