Construction of test Maxwell fields with scale symmetry

TL;DR

This paper shows that in spacetimes with self-similarity, the generators of scale symmetry can serve as vector potentials, producing Maxwell fields that inherit the background's scale invariance.

Contribution

It introduces a method to construct Maxwell test fields directly from spacetime self-similarity generators, linking geometric symmetry to electromagnetic solutions.

Findings

Maxwell equations are satisfied by homothetic vectors in self-similar spacetimes.

Constructed test fields exhibit the same scale symmetry as the background.

The approach provides a geometric way to generate electromagnetic solutions in symmetric spacetimes.

Abstract

Geometrical symmetry in a spacetime can generate test solutions to the Maxwell equation. We demonstrate that the source-free Maxwell equation is satisfied by any generator of spacetime self-similarity---a proper homothetic vector---identified with a vector potential of the Maxwell theory. The test fields obtained in this way share the scale symmetry of the background.