Generalised splitting of spacetime
type: Item
instance of: scholarly article
title: Generalised splitting of spacetime
zbMATH Open document ID: 0773.53054
DOI: 10.1007/BF00760433
author: D. McManus
published in: General Relativity and Gravitation
publication date: 1992-09-27T00:00:00Z
review text: The 3+1 splitting of space-time used by Arnowitt, Deser and Misner (ADM) is generalized to an \(m+n\) splitting. Thus, the foliating spaces are of arbitrary dimension \(m\) in a space-time of dimension \(m+n\). The shift vector and ADM lapse function are appropriately generalized and a derivation of the generalized Gauss-Codazzi and Gauss-Weingarten equations associated with such a splitting are derived. In addition, the projected components of the Ricci tensor are calculated. Finally, the author considers a globally orthogonal \(m+n\) splitting in which case the above equations assume a more manageable and elegant form. As the author acknowledges, such a study of foliating spaces has previously been done but the value of this paper is in its use of a language more accessible to physicists familiar with the ADM formalism.
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 53B30
Mathematics Subject Classification ID: 53B25
zbMATH DE Number: 64318
zbMATH Keywords: Gauss-Codazzi-equations
zbMATH Keywords: shift vector
zbMATH Keywords: lapse function
zbMATH Keywords: Gauss-Weingarten equations
zbMATH Keywords: Ricci tensor
zbMATH Keywords: ADM formalism
reviewed by: Dean E. Allison
MaRDI profile type: Publication
cites work: Ricci-Calculus
cites work: Quantum Theory of Gravity. I. The Canonical Theory
full work available at URL: https://doi.org/10.1007/bf00760433
OpenAlex ID: W2052533973
Recommended article: Q4206057
Recommended article: Split structures in general relativity
Recommended article: Splitting theorems for spatially closed space-times
Recommended article: Split structures in general relativity and the Kaluza–Klein theories
Recommended article: Q4550846
Recommended article: Segre decomposition of spacetimes
Recommended article: Q4394719
Recommended article: Q4263137
Recommended article: Generalising the coupling between spacetime and matter
Recommended article: Generalised space-time and gauge transformations
description: scientific article; zbMATH DE number 64318