On the convergence of Regge calculus to general relativity

Details On the convergence of Regge calculus to general relativity On the convergence of Regge calculus to general relativity

2000-06-05

arxiv.org/abs/gr-qc/0006017v2

Class.Quant.Grav. 18 (2001) 517-526

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Updated to match published version. Details of numerical calculations added, several sections rewritten. 9 pages, 4 EPS figure

Scientific paper

10.1088/0264-9381/18/3/311

Motivated by a recent study casting doubt on the correspondence between Regge calculus and general relativity in the continuum limit, we explore a mechanism by which the simplicial solutions can converge whilst the residual of the Regge equations evaluated on the continuum solutions does not. By directly constructing simplicial solutions for the Kasner cosmology we show that the oscillatory behaviour of the discrepancy between the Einstein and Regge solutions reconciles the apparent conflict between the results of Brewin and those of previous studies. We conclude that solutions of Regge calculus are, in general, expected to be second order accurate approximations to the corresponding continuum solutions.

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