M{\o}ller Energy-Momentum Complex of a Static Axially Symmetric Vacuum Space-Time

TL;DR

This paper compares different energy-momentum complexes in calculating energy and momentum densities for a static axially symmetric vacuum spacetime, highlighting discrepancies in energy density but consistency in momentum density across methods.

Contribution

It provides a comparative analysis of M{\

Findings

Different prescriptions yield varying energy densities.

All methods agree on momentum density.

Highlights limitations of certain energy-momentum complexes.

Abstract

The energy and momentum densities associated with the Weyl metric are calculated using M{\o}ller's energy-momentum complex. These results are compared with the results obtained by using the energy-momentum complexes of Einstein, Landau and Lifshitz, Papapetrou and Bergmann. We show that the aforementioned different prescriptions and that of M{\o}ller do not give the same energy density, while give the same momentum density.