Gravitational energy-momentum in small regions according to Moller's tetrad expression

TL;DR

This paper evaluates Moller's tetrad gravitational energy-momentum tensor in small vacuum regions and finds it proportional to the Bel-Robinson tensor, indicating positive energy properties.

Contribution

It demonstrates that Moller's tetrad energy-momentum tensor aligns with the Bel-Robinson tensor in small vacuum regions, confirming its positive energy characteristics.

Findings

Moller's tensor is proportional to the Bel-Robinson tensor in small regions.

The tensor satisfies the positivity property expected of gravitational energy.

The analysis uses Riemann normal coordinates and orthonormal frames.

Abstract

Moller's tetrad gravitational energy-momentum "tensor" is evaluated for a small vacuum region using an orthonormal frame adapted to Riemann normal coordinates. We find that it does satisfy the highly desired property of being a positive multiple of the Bel-Robinson tensor.