On a variational theory of light rays on Lorentzian manifolds

Fabio Giannoni; Antonio Masiello

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1995)

  • Volume: 6, Issue: 3, page 155-159
  • ISSN: 1120-6330

Abstract

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In this Note, by using a generalization of the classical Fermat principle, we prove the existence and multiplicity of lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds, satisfying a suitable compactness assumption, which is weaker than the globally hyperbolicity.

How to cite

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Giannoni, Fabio, and Masiello, Antonio. "On a variational theory of light rays on Lorentzian manifolds." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 6.3 (1995): 155-159. <http://eudml.org/doc/244145>.

@article{Giannoni1995,
abstract = {In this Note, by using a generalization of the classical Fermat principle, we prove the existence and multiplicity of lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds, satisfying a suitable compactness assumption, which is weaker than the globally hyperbolicity.},
author = {Giannoni, Fabio, Masiello, Antonio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Lorentzian manifolds; Lightlike geodesies; Fermât principle; Morse theory; Fermat's principle; causality conditions},
language = {eng},
month = {10},
number = {3},
pages = {155-159},
publisher = {Accademia Nazionale dei Lincei},
title = {On a variational theory of light rays on Lorentzian manifolds},
url = {http://eudml.org/doc/244145},
volume = {6},
year = {1995},
}

TY - JOUR
AU - Giannoni, Fabio
AU - Masiello, Antonio
TI - On a variational theory of light rays on Lorentzian manifolds
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1995/10//
PB - Accademia Nazionale dei Lincei
VL - 6
IS - 3
SP - 155
EP - 159
AB - In this Note, by using a generalization of the classical Fermat principle, we prove the existence and multiplicity of lightlike geodesics joining a point with a timelike curve on a class of Lorentzian manifolds, satisfying a suitable compactness assumption, which is weaker than the globally hyperbolicity.
LA - eng
KW - Lorentzian manifolds; Lightlike geodesies; Fermât principle; Morse theory; Fermat's principle; causality conditions
UR - http://eudml.org/doc/244145
ER -

References

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  9. HELFER, A., Conjugate points on spacelike geodesics or Pseudo-Self-Adjoint Morse-Sturm-Liouville operators. Preprint. Zbl0799.58018
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  12. MORSE, M., The Calculus of Variations in the Large. Coll. Lect.Am. Math. Soc., vol. 18, 1934. Zbl0011.02802
  13. O'NEILL, B., Semi-Riemannian Geometry with Applications to Relativity. Acad. Press Inc., New-York-London1983. Zbl0531.53051
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  15. PERLICK, V., On Fermat's principle in general relativity: I. The general case. Class. Quantum Grav., 7, 1990, 1319-1331. Zbl0707.53054MR1064182
  16. UHLENBECK, K., A Morse Theory for geodesics on a Lorentz manifold. Topology, 14, 1975, 69-90. Zbl0323.58010MR383461

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