Geodesic structure of standard static space--times.
type: Item
instance of: scholarly article
title: Geodesic structure of standard static space--times.
zbMATH Open document ID: 1034.53040
DOI: 10.1016/S0393-0440(02)00154-7
author: Dean E. Allison
author: Bülent Ünal
published in: Journal of Geometry and Physics
publication date: 2003-05-22T00:00:00Z
review text: For a Riemannian manifold \((F, g_F)\) and smooth \(f\colon (a,b)\to (0,\infty)\) define the standard static space time \((M,g)\) to be the product \(F\times (a,b)\) with the metric \(-f^2dt^2\oplus g_F\). The authors study various properties of geodesics of \((M,g)\). A manifold is said to satisfy the nonreturning property if for every point \(p\) there is an arbitrarily small neighborhood \(U(p)\) such that a geodesic leaving \(U(p)\) does not return to it. The authors prove that the standard static-space time \((M,g)\) satisfies the nonreturning property if and only if \((F, g_F)\) does satisfy it. They prove that if \(F\) is compact (or if \(\sup f < \infty\) and \((F,g_F)\) has a pseudoconvex geodesic system), then \((M,g)\) has a pseudoconvex geodesic system. As a corollary they get that if \(\sup f< \infty\) and \((F,g_F)\) has a pseudoconvex geodesic system and satisfies the nonreturning property, then the \((M,g)\) is geodesically connected.
Mathematics Subject Classification ID: 53C22
Mathematics Subject Classification ID: 53C50
zbMATH DE Number: 1915176
zbMATH Keywords: warped product
zbMATH Keywords: standard static space time
zbMATH Keywords: geodesic connectedness
zbMATH Keywords: nonreturning property
zbMATH Keywords: geodesic pseudoconvexity
zbMATH Keywords: Lorentz manifolds
MaRDI profile type: Publication
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full work available at URL: s0393-0440(02)00154-7
OpenAlex ID: W2065078886
description: scientific article; zbMATH DE number 1915176