no. 2
On the existence of geodesics in static Lorentz manifolds with singular boundary
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 2, pp. 255-289. 
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     title = {On the existence of geodesics in static {Lorentz} manifolds with singular boundary},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {255--289},
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     volume = {Ser. 4, 19},
     number = {2},
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     zbl = {0776.53040},
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Benci, V.; Fortunato, D.; Giannoni, F. On the existence of geodesics in static Lorentz manifolds with singular boundary. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 19 (1992) no. 2, pp. 255-289. http://www.numdam.org/item/ASNSP_1992_4_19_2_255_0/

[1] A. Avez, Essais de géométrie Riemanniene hyperbolique: Applications to the relativité générale, Ann. Inst. Fourier 132, (1963), 105-190. | Numdam | MR | Zbl

[2] V. Benci, Normal modes of a Lagrangian system constrained in a potential well, Ann. Inst. H. Poincaré Anal. Non Linéaire, 1, (1984), 379-400. | Numdam | MR | Zbl

[3] V. Benci - D. Fortunato, Existence of geodesics for the Lorentz metric of a stationary gravitational field, Ann. Inst. H. Poincaré Anal. Non Linéaire, 7, (1990), 27-35. | Numdam | MR | Zbl

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

[5] V. Benci - D. Fortunato - F. Giannoni, On the existence of multiple geodesics in static space-times, Ann. Inst. H. Poincaré Anal. Non Linéaire, 8, (1991), 79-102. | Numdam | MR | Zbl

[6] V. Benci - D. Fortunato - F. Giannoni, Some results on the existence of geodesics in Lorentz manifolds with nonsmooth boundary, Atti Accad. Naz. Lincei Rend. Cl. Sci. Fis. Mat. Natur., 2, (1991), 17-23. | MR | Zbl

[7] E. Fadell - A. Husseini, Category of loop spaces of open subsets in Euclidean space, preprint.

[8] E. Fadell - A. Husseini, Infinite cup length in free loop spaces with application to a problem of the N-body type, preprint.

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

[10] W. Klingenberg, Lectures on closed geodesics, Springer-Verlag, Berlin/Heidelberg /New-York, 1978. | MR | Zbl

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

[12] L. Landau - E. Lifchitz, Theorie des champs, Mir, Moscou, 1970. | MR

[13] J. Nash, The embedding problem for Riemannian manifolds, Ann. of Math. 63, (1956), 20-63. | MR | Zbl

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

[15] R.S. Palais, Critical point theory and the minimax principle, Global Anal., Proc. Sym. "Pure Math." 15, Amer. Math. Soc. (1970), 185-202. | MR | Zbl

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

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

[18] H.J. Seifert, Global connectivity by time-like geodesics, Z. Naturforsch. 22a, (1967), 1356-60. | MR | Zbl

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