On Energy Distribution of Two Space-times with Planar and Cylindrical Symmetries

TL;DR

This paper investigates the energy distribution in static plane-symmetric and cylindrically symmetric Einstein-Maxwell solutions using various energy-momentum complexes, finding finite results and supporting the localized energy hypothesis.

Contribution

It extends energy distribution studies to non-spherical symmetries using multiple complexes, revealing coincidences and supporting the Cooperstock hypothesis.

Findings

Energy expressions are finite and well-defined.

Einstein and Tolman prescriptions yield coincident results.

Supports the localized energy hypothesis.

Abstract

Considering encouraging Virbhadra's results about energy distribution of non-static spherically symmetric metrics in Kerr-Schild class, it would be interesting to study some space-times with other symmetries. Using different energy-momentum complexes, i.e. M{\o}ller, Einstein, and Tolman, in static plane-symmetric and cylindrically symmetric solutions of Einstein-Maxwell equations in 3+1 dimensions, energy (due to matter and fields including gravity) distribution is studied. Energy expressions are obtained finite and well-defined. calculations show interesting coincidences between the results obtained by Einstein and Tolamn prescriptions. Our results support the Cooperstock hypothesis about localized energy.