Geodesic
Some results on the existence of geodesics in static Lorentz manifolds with singular boundary
Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 2 (1991) no. 1, pp. 17-23.

Voir la notice de l'article provenant de la source Biblioteca Digitale Italiana di Matematica

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. 
@article{RLIN_1991_9_2_1_a1,
     author = {Benci, Vieri and Fortunato, Donato and Giannoni, Fabio},
     title = {Some results on the existence of geodesics in static {Lorentz} manifolds with singular boundary},
     journal = {Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni},
     pages = {17--23},
     publisher = {mathdoc},
     volume = {Ser. 9, 2},
     number = {1},
     year = {1991},
     zbl = {0737.53059},
     mrnumber = {167940},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/RLIN_1991_9_2_1_a1/}
}
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. Rendiconti Lincei. Matematica e applicazioni
PY  - 1991
SP  - 17
EP  - 23
VL  - 2
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/RLIN_1991_9_2_1_a1/
LA  - en
ID  - RLIN_1991_9_2_1_a1
ER  - 
%0 Journal Article
%A Benci, Vieri
%A Fortunato, Donato
%A Giannoni, Fabio
%T Some results on the existence of geodesics in static Lorentz manifolds with singular boundary
%J Atti della Accademia nazionale dei Lincei. Rendiconti Lincei. Matematica e applicazioni
%D 1991
%P 17-23
%V 2
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/RLIN_1991_9_2_1_a1/
%G en
%F RLIN_1991_9_2_1_a1
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. Rendiconti Lincei. Matematica e applicazioni, Série 9, Tome 2 (1991) no. 1, pp. 17-23. http://geodesic.mathdoc.fr/item/RLIN_1991_9_2_1_a1/

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

[2] V. Benci - D. Fortunato, Existence of geodesics for the Lorentz metric of a stationary gravitational field. Ann. Inst. H. Poincaré, Analyse non Lineaire, 7, 1990, 27-35. | fulltext mini-dml | MR | Zbl

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

[4] V. Benci - D. Fortunato - F. Giannoni, On the existence of multiple geodesics in static space-times. Ann. Inst. H. Poincaré, Analyse non Lineaire, to appear. | fulltext mini-dml | MR | Zbl

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

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

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

[8] B. O'Neill, Semi-Riemannian geometry with applications to relativity. Academic Press Inc., New York-London 1983. | MR | Zbl

[9] R. Penrose, Techniques of differential topology in relativity. Conf. Board Math. Sci., 7, S.I.A.M. Philadelphia 1972. | MR | Zbl

[10] J. T. Schwartz, Nonlinear functional analysis. Gordon and Breach, New York 1969. | MR | Zbl

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

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