Teleparallel Energy-Momentum Distribution of Locally Rotationally Symmetric Spacetimes

TL;DR

This paper investigates the energy-momentum distribution in locally rotationally symmetric spacetimes within teleparallel gravity, comparing various prescriptions and finding consistent momentum components across different metrics and prescriptions, with some variations in energy components.

Contribution

It provides a comprehensive analysis of energy-momentum distributions in LRS spacetimes using multiple teleparallel prescriptions, highlighting their similarities and differences.

Findings

Momentum densities are identical for Einstein, Bergmann-Thomson, and Møller prescriptions across all metrics.

Energy components are consistent for three prescriptions only in metrics I and II.

Møller energy-momentum distribution is independent of the teleparallel coupling constant.

Abstract

In this paper, we explore the energy-momentum distribution of locally rotationally symmetric (LRS) spacetimes in the context of the teleparallel theory of gravity by considering the three metrics, I, II and III, representing the whole class of LRS sapcetimes. In this regard, we use the teleparallel versions of the Einstein, Landau-Lifshitz, Bergmann-Thomson, and M$\ddot{o}$ller prescriptions. The results show that the momentum density components for the Einstein, Bergmann-Thomson, and M$\ddot{o}$ller prescriptions turn out to be same in all cases of the metrics I, II and III, but are different from those of the Landau- Lifshitz prescription, while the energy components remain the same for these three prescriptions only in all possible cases of the metrics I and II. We mention here that the M$\ddot{o}$ller energy-momentum distribution is independent of the coupling constant $\lambda$; that is, these results are valid for any teleparallel models.