On the gravitational energy of the Bonnor spacetime

TL;DR

This paper investigates the gravitational energy and flux in the Bonnor spacetime, demonstrating that they are non-zero outside the source using non-local expressions derived from the Einstein pseudotensor.

Contribution

It introduces non-local expressions from the Einstein pseudotensor to analyze gravitational energy in the Bonnor spacetime, showing it remains non-zero outside the source.

Findings

Gravitational energy and flux are non-zero outside the source.

Energy and flux do not vanish outside the material source.

Non-local expressions reveal persistent gravitational energy in this spacetime.

Abstract

In the paper we consider the energy and its flux in the Bonnor spacetime. We construct some non-local expressions from the Einstein canonical energy-momentum pseudotensor of the gravitational field which show that the gravitational energy and its flux in this spacetime are different from zero and do not vanish even outside of the material source (a stationary beam of the null dust) of this spacetime.