Some results on the existence of geodesics in static Lorentz manifolds with singular boundary
Benci, Vieri ; Fortunato, Donato ; Giannoni, Fabio
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni, Tome 2 (1991), p. 17-23 / Harvested from Biblioteca Digitale Italiana di Matematica
Access to full text
Full (PDF)
Full (DjVu)

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.

In questa Nota trattiamo il problema dell'esistenza di geodetiche congiungenti due assegnati punti di certe varietà di Lorentz non complete, delle quali lo spazio-tempo di Schwarzschild è l'esempio fisico più semplice.

Publié le : 1991-03-01
@article{RLIN_1991_9_2_1_17_0,
     author = {Vieri Benci and Donato Fortunato and Fabio Giannoni},
     title = {Some results on the existence of geodesics in static Lorentz manifolds with singular boundary},
     journal = {Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni},
     volume = {2},
     year = {1991},
     pages = {17-23},
     zbl = {0737.53059},
     mrnumber = {1120118},
     language = {en},
     url = {http://dml.mathdoc.fr/item/RLIN_1991_9_2_1_17_0}
}

Benci, Vieri; Fortunato, Donato; 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, Tome 2 (1991) pp. 17-23. http://gdmltest.u-ga.fr/item/RLIN_1991_9_2_1_17_0/

[1] Avez, A., Essais de geometrie Riemanniene hyperbolique: applications to the relativité generale. Ann. Inst. Fourier, 132, 1963, 105-90. | MR 167940 | Zbl 0188.54801

[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. | MR 1046082 | Zbl 0697.58011

[3] Benci, V. - Fortunato, D., On the existence of infinitely many geodesics on space-time manifolds. Adv. Math., to appear. | MR 1275190 | Zbl 0808.58016

[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. | MR 1094653 | Zbl 0716.53057

[5] Benci, V. - Fortunato, D. - Giannoni, F., On the existence of geodesics in Lorentz manifolds with singular boundary. Ist. Mat. Appl. Univ. Pisa, preprint. | Zbl 0776.53040

[6] Hawking, S. W. - Ellis, G.F., The large scale structure of space-time. Cambridge Univ. Press, 1973. | MR 424186 | Zbl 0265.53054

[7] Kruskal, M. D., Maximal extension of Schwarzschild metric. Phys. Rev., 119, 1960, 1743-1745. | MR 115757 | Zbl 0098.19001

[8] O'Neill, B., Semi-Riemannian geometry with applications to relativity. Academic Press Inc., New York-London1983. | MR 719023 | Zbl 0531.53051

[9] Penrose, R., Techniques of differential topology in relativity. Conf. Board Math. Sci., 7, S.I.A.M.Philadelphia1972. | MR 469146 | Zbl 0321.53001

[10] Schwartz, J. T., Nonlinear functional analysis. Gordon and Breach, New York1969. | MR 433481 | Zbl 0203.14501

[11] Seifert, H. J., Global connectivity by time-like geodesics. Z. Natureforsch, 22a, 1970, 1356-1360. | Zbl 0163.43701

[12] Uhlenbeck, K., A Morse theory for geodesics on a Lorentz manifold. Topology, 14, 1975, 69-90. | MR 383461 | Zbl 0323.58010