The Einstein field equation in a multidimensional universe
type: Item
instance of: scholarly article
title: The Einstein field equation in a multidimensional universe
zbMATH Open document ID: 0642.53088
DOI: 10.1007/BF00758971
author: Osmo Pekonen
published in: General Relativity and Gravitation
publication date: 1988-01-01T00:00:00Z
review text: String theory [\textit{M. B. Green}, \textit{J. H. Schwarz} and \textit{E. Witten}, Superstring theory: 1 and 2 (1987; Zbl 0619.53002)] predicts that the universe has 10 or 26 dimensions. A salient problem is how the Einstein field equation should be written in terms of these revivified Kaluza-Klein cosmologies. The answer is by now well-known, yet nobody seems to have rewritten the seminal computation in [\textit{D. Lovelock}, J. Math. Phys. 12, 498-501 (1971; Zbl 0213.488)] where an unnecessarily involved Euler-Lagrange variational method is employed and, curiously enough, no allusion to the Gauss-Bonnet-Chern theorem is made. We provide a more straightforward argument, which has been inspired by Hilbert's original derivation of the Einstein field equation.
Mathematics Subject Classification ID: 53C80
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 83E15
zbMATH DE Number: 4046626
zbMATH Keywords: String theory
zbMATH Keywords: Einstein field equation
zbMATH Keywords: Kaluza-Klein cosmologies
Wikidata QID: Q109936070
MaRDI profile type: Publication
cites work: Q4720334
cites work: Conservation laws and integrability conditions for gravitational and Yang-Mills field equations
cites work: Q3756080
cites work: The Einstein Tensor and Its Generalizations
description: scientific article; zbMATH DE number 4046626