Periodic trajectories for a class of Lorentz-metrics of a time-dependent gravitational field
type: Item
instance of: scholarly article
title: Periodic trajectories for a class of Lorentz-metrics of a time-dependent gravitational field
zbMATH Open document ID: 0681.53033
DOI: 10.1007/BF01446909
author: Carlo Greco
published in: Mathematische Annalen
publication date: 1990-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/164701
review text: We deal with the existence of timelike geodesics on the spacetime manifold \(({\mathbb{R}}^ 4,g)\), where the Lorentz tensor \(g=g(t,x)\) is T- periodic in t. By using a variant of a well-known curve shortening procedure, we show that there exists a timelike periodic trajectory on \(({\mathbb{R}}^ 4,g)\) i.e. a timelike geodesic \(z(s)=(t(s),x(s))\) such that \(x(s+1)=x(s)\) and \(t(s+1)=t(s)+T.\)
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 4115463
zbMATH Keywords: Lorentz metric
zbMATH Keywords: timelike periodic trajectory
zbMATH Keywords: timelike geodesics
MaRDI profile type: Publication
cites work: Existence of geodesics for the Lorentz metric of a stationary gravitational field
cites work: Q4181002
cites work: A Morse theory for geodesics on a Lorentz manifold
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description: scientific article; zbMATH DE number 4115463