On the Ricci curvature of compact spacelike hypersurfaces in Einstein conformally stationary-closed spacetimes
type: Item
instance of: scholarly article
title: On the Ricci curvature of compact spacelike hypersurfaces in Einstein conformally stationary-closed spacetimes
zbMATH Open document ID: 1020.83009
DOI: 10.1023/A:1022914101755
author: Juan A. Aledo
author: José A. Gálvez
published in: General Relativity and Gravitation
publication date: 2003-05-25T00:00:00Z
review text: The purpose of this paper is to establish a sufficient condition for a compact spacelike hypersurface \(M\) in a spacetime \(\overline M\) equipped with a timelike closed conformal vector field \(K\), to be a leaf of the foliation determined by \(K\), in terms of a pinching condition for its Ricci curvature. With this aim, an integral formula involving the Ricci and scalar curvatures of the hypersurface \(M\) (being \(\overline M\) non necessarily Einstein) is developed, which furthermore allows one to obtain several non-existence results. Moreover, some interesting consequences for the particular case, when \(\overline M\) is a generalized Robertson-Walker spacetime, are obtained.
Mathematics Subject Classification ID: 83C05
Mathematics Subject Classification ID: 53Z05
Mathematics Subject Classification ID: 83F05
zbMATH DE Number: 1915850
zbMATH Keywords: Einstein conformally stationary-closed spacetime
zbMATH Keywords: compact spacelike hypersurface
zbMATH Keywords: Lorentzian manifold
zbMATH Keywords: integral formula
zbMATH Keywords: pinching condition
zbMATH Keywords: Ricci curvature
zbMATH Keywords: generalized Robertson-Walker spacetime
zbMATH Keywords: foliation
reviewed by: Serguey M. Pokas
MaRDI profile type: Publication
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full work available at URL: a:1022914101755
OpenAlex ID: W2144494881
description: scientific article; zbMATH DE number 1915850