Is the Regge Calculus a consistent approximation to General Relativity?

Abstract

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.

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

References in corpus (4)

• A fully (3+1)-D Regge calculus model of the Kasner cosmology
• Riemann Normal Coordinates, Smooth Lattices and Numerical Relativity
• Regge Calculus as a Fourth Order Method in Numerical Relativity
• An ADM 3+1 formulation for Smooth Lattice General Relativity

Cited by in corpus (8)

• A cosmological solution of Regge calculus
• On the convergence of Regge calculus to general relativity
• De Sitter horizon entropy from a simplicial Lorentzian path integral
• Modified Regge calculus as an explanation of dark energy
• Fast algorithms for computing defects and their derivatives in the Regge calculus
• Event and Apparent Horizon Finders for 3+1 Numerical Relativity
• End of a Dark Age?
• Evolutions of Gowdy, Brill and Teukolsky initial data on a smooth lattice