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Causal cells: spacetime polytopes with null hyperfaces · Around

2012

Causal cells: spacetime polytopes with null hyperfaces

Neiman, Yasha

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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.

Built on

T. Regge, “General Relativity Without Coordinates,” Nuovo Cim. 19
1961
Earlier work this paper cites.
R. Penrose and W. Rindler, “Spinors And Space-time. 1. Two Spinor Calculus And Relativistic Fields,” Chapter 1, Cambridge, Uk: Univ. Pr. (1984) 458 P. (Cambridge Monographs On Mathematical Physics)
1984
Earlier work this paper cites.

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B. Z. Foster and T. Jacobson, “Propagating spinors on a tetrahedral spacetime lattice,” hep-th/0310166
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J. Ambjorn, J. Jurkiewicz and R. Loll, “Causal Dynamical Triangulations and the Quest for Quantum Gravity,” arXiv:1004.0352 [hep-th]
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C. Rovelli, “Zakopane lectures on loop gravity,” [arXiv:1102.3660 [gr-qc]]
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Then

R. Loll, “Discrete Lorentzian quantum gravity,” Nucl. Phys. Proc. Suppl. 94
2001
Later among the works it cites.
A. P. Gentle, “Regge calculus: A Unique tool for numerical relativity,” Gen. Rel. Grav. 34
Original
2002
Later among the works it cites.

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