New positive small vacuum region gravitational energy expressions

TL;DR

This paper introduces numerous new gravitational energy-momentum pseudotensors that are positive in small vacuum regions and have good asymptotic limits, advancing the understanding of gravitational energy localization.

Contribution

It constructs an infinite family of holonomic quasi-local gravitational energy-momentum pseudotensors with desirable positivity and limit properties.

Findings

All pseudotensors are positive multiples of the Bel-Robinson tensor in small vacuum regions.

They possess good asymptotic limits both in matter and vacuum.

The approach enhances the theoretical framework for gravitational energy localization.

Abstract

We construct an infinite number of new holonomic quasi-local gravitational energy-momentum density pseudotensors with good limits asymptotically and in small regions, both materially and in vacuum. For small vacuum regions they are all a positive multiple of the Bel-Robinson tensor and consequently have positive energy.