The global structure of simple space-times
type: Item
instance of: scholarly article
title: The global structure of simple space-times
zbMATH Open document ID: 0683.53056
DOI: 10.1007/BF01244016
author: Richard P. A. C. Newman
published in: Communications in Mathematical Physics
publication date: 1989-01-01T00:00:00Z
review text: According to the author a space-time satisfying the chronology condition is called simple if it is equipped with future and past null infinities \({\mathcal I}^+\) and \({\mathcal I}^-\) in the usual way such that all endless null geodesics originate from \({\mathcal I}^-\) and end at \({\mathcal I}^+\). This situation is more general than that of an asymptotically simple and empty space-time [see the book of \textit{S. W. Hawking} and \textit{G. F. R. Ellis}, The large scale structure of space-time (Cambridge University Press. XI, 1973, Zbl 0265.53054)] where \({\mathcal I}^+\) and \({\mathcal I}^-\) are required to satisfy the condition of strong causality. The objective of this paper is to identify the principal causal and topological properties of simple space-times. Main goal is to generalize the topological classifications, obtained by R. Penrose, R. Geroch, S. W. Hawking and G. F. R. Ellis under additional constraints on the structure of the null infinities, to the case of simple space-times. The topological structure of such a space-time is characterized by the author as follows: \({\mathcal I}^+\) is diffeomorphic to the complement of a point in some contractible open 3-manifold, the strongly causal region \({\mathcal I}^+_ 0\) of \({\mathcal I}^+\) is diffeomorphic to \(S^ 2\times {\mathbb{R}}\), and every compact connected spacelike 2-surface in \({\mathcal I}^+\) is contained in \({\mathcal I}^+_ 0\) and is a strong deformation retract of both \({\mathcal I}^+_ 0\) and \({\mathcal I}^+\). Moreover, the space-time must be globally hyperbolic with Cauchy surfaces which, subject to the truth of the Poincaré conjecture, are diffeomorphic to \({\mathbb{R}}^ 3\). In addition to these main results the paper contains a lot of other useful information on the geometrical structure of simple space-times.
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 57N13
zbMATH DE Number: 4119159
zbMATH Keywords: chronology condition
zbMATH Keywords: null infinities
zbMATH Keywords: simple space-times
zbMATH Keywords: topological classifications
zbMATH Keywords: strongly causal region
zbMATH Keywords: strong deformation retract
zbMATH Keywords: globally hyperbolic
reviewed by: Bernd Wegner
MaRDI profile type: Publication
cites work: Zero rest-mass fields including gravitation: asymptotic behaviour
cites work: The Large Scale Structure of Space-Time
cites work: Q5522742
cites work: Q4084319
cites work: An R 4 spacetime with a Cauchy surface which is not R 3
cites work: Q5825483
cites work: The topology of four-dimensional manifolds
cites work: Q4160083
cites work: Cartesian products of contractible open manifolds
cites work: Locally euclidean factors of \(E^ 4\) which cannot be imbedded in \(E^ 3\)
cites work: Foundational Essays on Topological Manifolds, Smoothings, and Triangulations. (AM-88)
cites work: Q5584509
description: scientific article; zbMATH DE number 4119159