1999/07/31 by Steven G. Harris · 1 citation
Physics and Astronomy · #gr-qc
paper · pdf · doi:10.1088/0264-9381/17/3/303
published as Class.Quant.Grav. 17 (2000) 551-603 · 56 pages, AMS-TeX; 1 page of figure captions (TeX); 22 figures, EPS format; to be published in Quantum Class. Grav.; principal reason for replacement is to have the figures included (also, introduction is expanded slightly, and one example is simplified)
arxiv created 1999/11/10 · arxiv updated 2009/11/30
A method is presented for imputing a topology for any chronological set, i.e., a set with a chronology relation, such as a spacetime or a spacetime with some sort of boundary. This topology is shown to have several good properties, such as replicating the manifold topology for a spacetime and replicating the expected topology for some simple examples of spacetime-with-boundary; it also allows for a complete categorical characterization, in topological categories, of the Future Causal Boundary construction of Geroch, Kronheimer, and Penrose, showing that construction to have a universal property for future-completing chronological sets with spacelike boundaries. Rigidity results are given for any reasonable future completion of a spacetime, in terms of the GKP boundary: In the imputed topology, any such boundary must be homeomorphic to the GKP boundary (if all points have indecomposable pasts) or to a topological quotient of a closely related boundary (if boundaries are spacelike). A large class of warped-product-type spacetimes with spacelike boundaries is examined, calculating the GKP and other possible boundaries, and showing that the imputed topology gives expected results; included among these are the Schwarzschild singularity and those Robertson-Walker singularities which are spacelike.