A remark about static space times
type: Item
instance of: scholarly article
title: A remark about static space times
zbMATH Open document ID: 1162.53051
author: Jacques Lafontaine
published in: Journal of Geometry and Physics
publication date: 2009-01-21T00:00:00Z
review text: The author studies the equation \[ Ddf+(\Delta f)g-f\operatorname{Ric}=0 \] well known in general relativity, whose unknowns are the metric \(g\) and the non-identically vanishing function \(f\), on a compact manifold \(M\). Mainly, he proves the following Theorem: Let \((M,g)\) be a compact three dimensional Riemannian manifold such that \(S(g)\) has two linearly independent solutions. Then \((M,g)\) is isometric to a standard product \(S^{1}\times S^{2}\), \(S^{1}\times \mathbb{P}^{2} \mathbb{R}\) or the standard 3-sphere.
reviewed by: Cihan Özgür
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C25
Mathematics Subject Classification ID: 83C15
Mathematics Subject Classification ID: 83C20
zbMATH DE Number: 5495737
zbMATH Keywords: scalar curvature
zbMATH Keywords: static space-time
MaRDI profile type: Publication
full work available at URL: j.geomphys.2008.09.005
OpenAlex ID: W2046317664
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DOI: 10.1016/J.GEOMPHYS.2008.09.005
description: scientific article