A Fermat principle on Lorentzian manifolds and applications
type: Item
instance of: scholarly article
title: A Fermat principle on Lorentzian manifolds and applications
zbMATH Open document ID: 0855.53038
DOI: 10.1016/0893-9659(96)00019-5
author: Flavia Antonacci
author: Paolo Piccione
published in: Applied Mathematics Letters
publication date: 1997-02-03T00:00:00Z
review text: The authors present a variational principle for lightlike geodesics joining a point to a timelike curve in a Lorentzian manifold. For the techniques used it is essential that the Lorentzian manifold is assumed to admit a global time function, i.e., to be stably causal. If a certain precompactness condition is satisfied, standard results of Lyusternik-Schnirelman theory imply existence and multiplicity results for such lightlike geodesics. Proofs of the statements are only sketched and a more detailed paper is announced to appear elswhere.
reviewed by: Volker Perlick
Mathematics Subject Classification ID: 53C50
Mathematics Subject Classification ID: 58E10
Mathematics Subject Classification ID: 83C10
Mathematics Subject Classification ID: 53C22
zbMATH DE Number: 915083
zbMATH Keywords: Fermat principle
zbMATH Keywords: Lorentz manifold
zbMATH Keywords: lightlike geodesics
MaRDI profile type: Publication
full work available at URL: 0893-9659(96)00019-5
OpenAlex ID: W2031766299
cites work: Q4486827
cites work: On Fermat's principle in general relativity. I. The general case
cites work: On Fermat's principle in general relativity. II. The conformally stationary case
cites work: A Morse theory for geodesics on a Lorentz manifold
cites work: Q4146134
cites work: Q3312869
description: scientific article; zbMATH DE number 915083