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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.Comment: Accepted in Classical and Quantum Gravit
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