New electromagnetic conservation laws

TL;DR

This paper proves new symmetry and conservation properties of the Chevreton superenergy tensor in electromagnetic fields, revealing it as a conserved, trace-free tensor distinct from energy-momentum, applicable in Einstein-Maxwell spacetimes.

Contribution

It establishes that the Chevreton tensor is symmetric and divergence-free without currents, and introduces its trace as a new conserved tensor in Einstein-Maxwell theory.

Findings

Chevreton tensor is completely symmetric without electromagnetic currents.

The trace of the Chevreton tensor is divergence-free and conserved.

This tensor differs from the energy-momentum tensor and applies to test fields and Einstein-Maxwell spacetimes.

Abstract

The Chevreton superenergy tensor was introduced in 1964 as a counterpart, for electromagnetic fields, of the well-known Bel-Robinson tensor of the gravitational field. We here prove the unnoticed facts that, in the absence of electromagnetic currents, Chevreton's tensor (i) is completely symmetric, and (ii) has a trace-free divergence if Einstein-Maxwell equations hold. It follows that the trace of the Chevreton tensor is a rank-2, symmetric, trace-free, {\em conserved} tensor, which is different from the energy-momentum tensor, and nonetheless can be constructed for any test Maxwell field, or any Einstein-Maxwell spacetime.