Does three dimensional electromagnetic field inherit the spacetime symmetries?

TL;DR

This paper proves that in certain (1+2)-dimensional Einstein-Maxwell theories, the electromagnetic field always inherits the spacetime symmetries, even with complex Lagrangians including Chern-Simons terms.

Contribution

It establishes a general symmetry inheritance result for electromagnetic fields in (1+2)-dimensional spacetimes with broad classes of Einstein-Maxwell theories.

Findings

Electromagnetic fields inherit spacetime symmetries in the studied theories.

The result holds for theories with diff-covariant gravitational Lagrangians including Chern-Simons terms.

Applies to a large class of generalized Einstein-Maxwell models.

Abstract

We prove that the electromagnetic field in a (1+2)-dimensional spacetime necessarily inherits the symmetries of the spacetime metric in a large class of generalized Einstein-Maxwell theories. The Lagrangians of the studied theories have general diff-covariant gravitational part and include both the gravitational and the gauge Chern-Simons terms.