Is the Regge Calculus a consistent approximation to General Relativity?

Details Is the Regge Calculus a consistent approximation to General Relativity? Is the Regge Calculus a consistent approximation to General Relativity?

1995-02-27

arxiv.org/abs/gr-qc/9502043v2

Gen.Rel.Grav. 32:897-918,2000

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

27 pages, plain TeX, very belated update to match journal article

Scientific paper

We will ask the question of whether or not the Regge calculus (and two related simplicial formulations) is a consistent approximation to General Relativity. Our criteria will be based on the behaviour of residual errors in the discrete equations when evaluated on solutions of the Einstein equations. We will show that for generic simplicial lattices the residual errors can not be used to distinguish metrics which are solutions of Einstein's equations from those that are not. We will conclude that either the Regge calculus is an inconsistent approximation to General Relativity or that it is incorrect to use residual errors in the discrete equations as a criteria to judge the discrete equations.

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