Physical decomposition of the gauge and gravitational fields

TL;DR

This paper extends a physical decomposition approach from gauge fields to gravity, providing a clear separation of geometric and physical components to address longstanding issues of defining gravitational energy.

Contribution

It introduces a unique decomposition of the metric into geometric and physical parts, resolving ambiguities in gravitational energy definitions.

Findings

Decomposition yields unambiguous gravitational energy expressions.

Rescues pseudo-tensors to produce definite physical results.

Relates to the transverse-traceless (TT) decomposition.

Abstract

Physical decomposition of the non-Abelian gauge field has recently solved the two-decade-lasting problem of a meaningful gluon spin. Here we extend this approach to gravity and attack the century-lasting problem of a meaningful gravitational energy. The metric is unambiguously separated into a pure geometric term which contributes null curvature tensor, and a physical term which represents the true gravitational effect and always vanishes in a flat space-time. By this decomposition the conventional pseudo-tensors of the gravitational stress-energy are easily rescued to produce definite physical result. Our decomposition applies to any symmetric tensor, and has interesting relation to the transverse-traceless (TT) decomposition discussed by Arnowitt, Deser and Misner, and by York.