The Space of Geodesics of a Lorentzian Manifold
September 28, 2013, update September 28, 2013
Here are two letters that I wrote to Serge Tabachnikov in May 2006, after we had a discussion on the structure of the space of null geodesics in lorentzian spaces. In these notes I explained how I build the space of non parametrized geodesics of a Minkowski space and how to equip it with a “conformal co-symplectic” structure. This structure gives, by the way, a canonical contact structure on the subspace of null geodesics, and, by inversion, the standard symplectic structure on the subspace of time/space-like geodesics.

These notes are cited in the paper that Serge published with Boris Khesin on “Pseudo-Riemannian geodesics and billiards”. After having noticed that these results began to be cited in some papers I thought it could be good to publish my notes somewhere, before writing down a paper for real. Here is a good place.

Reference for these documents: