Coupling Non-Gravitational Fields with Simplicial Spacetimes

Details Coupling Non-Gravitational Fields with Simplicial Spacetimes Coupling Non-Gravitational Fields with Simplicial Spacetimes

2010-02-26

arxiv.org/abs/1002.5001v2

Class. Quantum Grav.27:095011,2010

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

10 pages, no figures, Latex, fixed typos and minor corrections.

Scientific paper

10.1088/0264-9381/27/9/095011

The inclusion of source terms in discrete gravity is a long-standing problem. Providing a consistent coupling of source to the lattice in Regge Calculus (RC) yields a robust unstructured spacetime mesh applicable to both numerical relativity and quantum gravity. RC provides a particularly insightful approach to this problem with its purely geometric representation of spacetime. The simplicial building blocks of RC enable us to represent all matter and fields in a coordinate-free manner. We provide an interpretation of RC as a discrete exterior calculus framework into which non-gravitational fields naturally couple with the simplicial lattice. Using this approach we obtain a consistent mapping of the continuum action for non-gravitational fields to the Regge lattice. In this paper we apply this framework to scalar, vector and tensor fields. In particular we reconstruct the lattice action for (1) the scalar field, (2) Maxwell field tensor and (3) Dirac particles. The straightforward application of our discretization techniques to these three fields demonstrates a universal implementation of coupling source to the lattice in Regge calculus.

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