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

  • Robert J. Low
Part of the Lecture Notes in Physics book series (LNP, volume 692)


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 2s, and the relationships between these S 2s reflect causal relationships 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 2s 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.


Minkowski Space Quotient Space Causal Structure Cotangent Bundle Null Geodesic 
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© Springer 2006

Authors and Affiliations

  • Robert J. Low
    • 1
  1. 1.Mathematics Group, School of MISCoventry UniversityCoventryU.K.

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