New conservation laws for electromagnetic fields in gravity

TL;DR

This paper introduces a new tensor for source-free electromagnetic fields in Einstein spaces, leading to novel conservation laws that extend beyond traditional energy-momentum tensor symmetries.

Contribution

It presents a new divergence-free tensor applicable to various Einstein-Maxwell spacetimes, enabling the discovery of additional conserved quantities.

Findings

New tensor explicitly constructed and analyzed in special cases

Conserved currents derived from the new tensor can be non-trivial where traditional methods fail

Application to classical electrodynamics and specific solutions like Reissner-Nordström

Abstract

A recently found (gr-qc/0303036) 2-index, symmetric, trace-free, divergence-free tensor is introduced for arbitrary source-free electromagnetic fields. The tensor can be constructed for any test Maxwell field in Einstein spaces (including proper vacuum), and more importantly for any Einstein-Maxwell spacetime. The tensor is explicitly given and analyzed in some special situations, such as general null electromagnetic fields, Reissner-Nordstr\"om solution, or classical electrodynamics. We present an explicit example where the conserved currents derived from the energy-momentum tensor using symmetries are trivial, but those derived from the new tensor are not.