Equivalence of the Regge and Einstein equations for almost flat simplicial space-times

Leo Brewin

Research output: Contribution to journalArticleResearchpeer-review


The theory of distributions is applied to almost flat simplicial space-times. Explicit expressions are given for the first-order defects. It is shown explicitly that the Riemann tensor for an almost flat simplicial space-time contains delta-functions on the bones and derivatives of delta-functions on the 3-dimensional faces of the boundary of the space-time. The latter terms have not previously been seen in the Regge calculus. It is shown that the Regge and Hilbert actions have equal values on almost fiat simplicial space-times and that the Einstein equations lead directly to the Regge field equations.

Original languageEnglish
Pages (from-to)565-583
Number of pages19
JournalGeneral Relativity and Gravitation
Issue number6
Publication statusPublished - 1 Jun 1989

Cite this