Conservation Laws and Stress-energy-momentum Tensors for Systems with Background Fields

TL;DR

This paper clarifies how background structures and symmetries influence the construction of stress-energy-momentum tensors in diffeomorphism invariant theories, highlighting differences in their physical interpretations and conservation laws.

Contribution

It introduces an intrinsic coordinate independent framework to distinguish between various stress-energy-momentum tensors, emphasizing the role of background fields in their formulation.

Findings

Differentiates between Belinfante-Rosenfeld and Einstein-Hilbert tensors

Highlights the impact of background structures on conservation laws

Provides a unified perspective on stress-energy tensors in media

Abstract

This article attempts to delineate the roles played by non-dynamical background structures and Killing symmetries in the construction of stress-energy-momentum tensors generated from a diffeomorphism invariant action density. An intrinsic coordinate independent approach puts into perspective a number of spurious arguments that have historically lead to the main contenders, viz the Belinfante-Rosenfeld stress-energy-momentum tensor derived from a Noether current and the Einstein-Hilbert stress-energy-momentum tensor derived in the context of Einstein's theory of general relativity. Emphasis is placed on the role played by non-dynamical background (phenomenological) structures that discriminate between properties of these tensors particularly in the context of electrodynamics in media. These tensors are used to construct conservation laws in the presence of Killing Lie-symmetric background fields.