Genericity of nondegeneracy for light rays in stationary spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic γ : [0, 1] → M joining p and U whose endpoints are conjugate along γ . Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.