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Causal cells: spacetime polytopes with null hyperfaces
- Publication Year :
- 2012
-
Abstract
- We consider polyhedra and 4-polytopes in Minkowski spacetime - in particular, null polyhedra with zero volume, and 4-polytopes that have such polyhedra as their hyperfaces. We present the basic properties of several classes of null-faced 4-polytopes: 4-simplices, "tetrahedral diamonds" and 4-parallelotopes. We propose a "most regular" representative of each class. The most-regular parallelotope is of particular interest: its edges, faces and hyperfaces are all congruent, and it features both null hyperplanes and null segments. A tiling of spacetime with copies of this polytope can be viewed alternatively as a lattice with null edges, such that each point is at the intersection of four lightrays in a tetrahedral pattern. We speculate on the relevance of this construct for discretizations of curved spacetime and for quantum gravity.<br />Comment: 24 pages, 6 figures; submitted to Geometriae Dedicata; v2: added references
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1212.2916
- Document Type :
- Working Paper
- Full Text :
- https://doi.org/10.1007/s10711-012-9823-0