On the energy density of linearly polarized, plane gravitational wave

TL;DR

This paper investigates the energy density of linearly polarized plane gravitational waves using Einstein and Møller's pseudotensor prescriptions across different coordinate systems, revealing that energy component vanishes in null coordinates.

Contribution

It provides a comparative analysis of energy distribution of gravitational waves in various coordinate systems using two pseudotensor methods, highlighting coordinate-dependent energy results.

Findings

Energy density varies with coordinate choice

Energy component is zero in null coordinates

Different pseudotensor prescriptions yield consistent results

Abstract

In this article, the energy density of plane gravitational wave is studied by using Einstein and M{\o}ller's prescription of energy-momentum pseudotensors. The linearly polarized plan gravitational wave solution of Einstein field equation, which has been defined by Bondi et al., is represented by four kinds of different coodrinates. The energy distribution of gravitational wave solution in Einstein and M{\o}ller's prescription are obtained. Particularly the energy component is zero in null coordinates.