The Space of Null Geodesics (and a New Causal Boundary) [chapter]

Robert Low
Analytical and Numerical Approaches to Mathematical Relativity  
The space of null geodesics, G, of a space-time, M, carries information on various aspects of the causal structure M. In this contribution, we will review the space of null geodesics, G, and some natural structures which it carries, and see how aspects of the causal structure of M are encoded there. If M is strongly causal, then G has a natural contact manifold structure, points are represented in G by smooth Legendrian S 2 s, and the relationships between these S 2 s reflect causal
more » ... s between the points of M. One can also attempt to pass in the opposite direction with the intention of constructing a space-time from a family of S 2 s in G; this process suggests a means of attaching end-points to null geodesics of M, and thereby constructing a causal boundary. We close by summarizing some open questions in this general area.
doi:10.1007/11550259_2 fatcat:wex6vylf3vap7cehefgbbofo5u