Do electromagnetic waves always propagate along null geodesics?

TL;DR

This paper derives exact solutions to Maxwell's equations in various curved spacetimes, revealing that electromagnetic wave propagation aligns with null geodesics in non-rotating spheres but not in G"odel or Kerr spacetimes.

Contribution

It provides explicit solutions and demonstrates that electromagnetic waves do not always follow null geodesics in rotating or non-spherical spacetimes.

Findings

Electromagnetic waves follow null geodesics in non-rotating spherical spacetimes.

In G"odel and Kerr spacetimes, electromagnetic waves deviate from null geodesic paths.

Exact solutions for electromagnetic waves are constructed in different gravitational backgrounds.

Abstract

We find exact solutions to Maxwell equations written in terms of four-vector potentials in non--rotating, as well as in G\"odel and Kerr spacetimes. We show that Maxwell equations can be reduced to two uncoupled second-order differential equations for combinations of the components of the four-vector potential. Exact electromagnetic waves solutions are written on given gravitational field backgrounds where they evolve. We find that in non--rotating spherical symmetric spacetimes, electromagnetic waves travel along null geodesics. However, electromagnetic waves on G\"odel and Kerr spacetimes do not exhibit that behavior.