Do electromagnetic waves always propagate along null geodesics?
  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. 
Felipe A. Asenjo and Sergio A. Hojman
gr-qc