Ray-optical structures on Lorentzian manifolds

Abstract

In Chap. 5 we have established the notion of a ray-optical structure on a bare manifold $\mathcal{M}$. From now on we shall assume that there is a Lorentzian metric g given on $\mathcal{M}$. This metric is to be interpreted as a spacetime metric in the sense of general relativity, although for the mathematical formalism it will not be necessary to specialize to the case dim$(\mathcal{M}) = 4$. We shall assume, however, that dim$(\mathcal{M}) > 2$ > 2 to exclude some pathologies.