Some results on the existence of geodesics in static Lorentz manifolds with singular boundary

Vieri Benci; Donato Fortunato; Fabio Giannoni

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni (1991)

  • Volume: 2, Issue: 1, page 17-23
  • ISSN: 1120-6330

Abstract

top
In this Note we deal with the problem of the existence of geodesies joining two given points of certain non-complete Lorentz manifolds, of which the Schwarzschild spacetime is the simplest physical example.

How to cite

top

Benci, Vieri, Fortunato, Donato, and Giannoni, Fabio. "Some results on the existence of geodesics in static Lorentz manifolds with singular boundary." Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni 2.1 (1991): 17-23. <http://eudml.org/doc/244263>.

@article{Benci1991,
abstract = {In this Note we deal with the problem of the existence of geodesies joining two given points of certain non-complete Lorentz manifolds, of which the Schwarzschild spacetime is the simplest physical example.},
author = {Benci, Vieri, Fortunato, Donato, Giannoni, Fabio},
journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
keywords = {Lorentz manifolds; Geodesies; Critical points; critical points; geodesics; singular boundary; physical spacetimes},
language = {eng},
month = {3},
number = {1},
pages = {17-23},
publisher = {Accademia Nazionale dei Lincei},
title = {Some results on the existence of geodesics in static Lorentz manifolds with singular boundary},
url = {http://eudml.org/doc/244263},
volume = {2},
year = {1991},
}

TY - JOUR
AU - Benci, Vieri
AU - Fortunato, Donato
AU - Giannoni, Fabio
TI - Some results on the existence of geodesics in static Lorentz manifolds with singular boundary
JO - Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
DA - 1991/3//
PB - Accademia Nazionale dei Lincei
VL - 2
IS - 1
SP - 17
EP - 23
AB - In this Note we deal with the problem of the existence of geodesies joining two given points of certain non-complete Lorentz manifolds, of which the Schwarzschild spacetime is the simplest physical example.
LA - eng
KW - Lorentz manifolds; Geodesies; Critical points; critical points; geodesics; singular boundary; physical spacetimes
UR - http://eudml.org/doc/244263
ER -

References

top
  1. AVEZ, A., Essais de geometrie Riemanniene hyperbolique: applications to the relativité generale. Ann. Inst. Fourier, 132, 1963, 105-90. Zbl0188.54801MR167940
  2. BENCI, V. - FORTUNATO, D., Existence of geodesics for the Lorentz metric of a stationary gravitational field. Ann. Inst. H. Poincaré, Analyse non Lineaire, 7, 1990, 27-35. Zbl0697.58011MR1046082
  3. BENCI, V. - FORTUNATO, D., On the existence of infinitely many geodesics on space-time manifolds. Adv. Math., to appear. Zbl0808.58016MR1275190DOI10.1006/aima.1994.1036
  4. BENCI, V. - FORTUNATO, D. - GIANNONI, F., On the existence of multiple geodesics in static space-times. Ann. Inst. H. Poincaré, Analyse non Lineaire, to appear. Zbl0716.53057MR1094653
  5. BENCI, V. - FORTUNATO, D. - GIANNONI, F., On the existence of geodesics in Lorentz manifolds with singular boundary. Ist. Mat. Appl. Univ. Pisa, preprint. Zbl0776.53040
  6. HAWKING, S. W. - ELLIS, G.F., The large scale structure of space-time. Cambridge Univ. Press, 1973. Zbl0265.53054MR424186
  7. KRUSKAL, M. D., Maximal extension of Schwarzschild metric. Phys. Rev., 119, 1960, 1743-1745. Zbl0098.19001MR115757
  8. O'NEILL, B., Semi-Riemannian geometry with applications to relativity. Academic Press Inc., New York-London1983. Zbl0531.53051MR719023
  9. PENROSE, R., Techniques of differential topology in relativity. Conf. Board Math. Sci., 7, S.I.A.M.Philadelphia1972. Zbl0321.53001MR469146
  10. SCHWARTZ, J. T., Nonlinear functional analysis. Gordon and Breach, New York1969. Zbl0203.14501MR433481
  11. SEIFERT, H. J., Global connectivity by time-like geodesics. Z. Natureforsch, 22a, 1970, 1356-1360. Zbl0163.43701
  12. UHLENBECK, K., A Morse theory for geodesics on a Lorentz manifold. Topology, 14, 1975, 69-90. Zbl0323.58010MR383461

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.