On the existence of multiple geodesics in static space-times
Annales de l'I.H.P. Analyse non linéaire, Volume 8 (1991) no. 1, p. 79-102
@article{AIHPC_1991__8_1_79_0,
     author = {Benci, Vieri and Fortunato, Donato and Giannoni, Fabio},
     title = {On the existence of multiple geodesics in static space-times},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Gauthier-Villars},
     volume = {8},
     number = {1},
     year = {1991},
     pages = {79-102},
     zbl = {0716.53057},
     mrnumber = {1094653},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_1991__8_1_79_0}
}
Benci, V.; Fortunato, D.; Giannoni, F. On the existence of multiple geodesics in static space-times. Annales de l'I.H.P. Analyse non linéaire, Volume 8 (1991) no. 1, pp. 79-102. http://www.numdam.org/item/AIHPC_1991__8_1_79_0/

[1] S.I. Alber, The Topology of Functional Manifolds and the Calculus of Variations in the Large, Russian Math. Surv., Vol. 25, 1970, p. 51-117. | MR 279832 | Zbl 0222.58002

[2] A. Avez, Essais de géométrie Riemanniene hyperbolique: Applications to the relativité générale, Inst. Fourier, Vol. 132, 1963, p. 105-190. | Numdam | MR 167940 | Zbl 0188.54801

[3] P. Bartolo, V. Benci, and D. Fortunato, Abstract Critical Point Theorems and Applications to Some Nonlinear Problems with "Strong Resonance" at Infinity,Nonlinear Anal. T.M.A., Vol. 7, 1983, pp. 981-1012. | MR 713209 | Zbl 0522.58012

[4] J.K. Beem and P. Erlich, Global Lorentzian Geometry, M. Dekker, Pure Appl. Math., Vol. 67, 1981. | MR 619853 | Zbl 0462.53001

[5] V. Benci, Periodic Solutions of Lagrangian Systems on Compact Manifold, J. Diff. Eq., Vol. 63, 1986, pp. 135-161. | MR 848265 | Zbl 0605.58034

[6] V. Benci and D. Fortunato, Existence of Geodesics for the Lorentz Metric of a Stationary Gravitational Field, Ann. Inst. H. Poincaré, Anal. non linéaire, Vol. 7, 1990, pp. 27-35. | Numdam | MR 1046082 | Zbl 0697.58011

[7] V. Benci and D. Fortunato, Periodic Trajectories for the Lorentz Metric of a Static Gravitational Field, Proc. on "Variational Problems", Paris, June 1988 (to appear). | MR 1205170 | Zbl 0719.58009

[8] V. Benci and D. Fortunato, On the Existence of Infinitely Many Geodesics on Space-Time Manifolds, preprint, Dip. Mat. Univ. Bari, 1989. | MR 1275190

[9] V. Benci, D. Fortunato and F. Giannoni, On the Existence of Geodesics in Static Lorentz Manifolds with Nonsmooth Boundary, preprint. Ist. Mat. Appl. Univ. Pisa.

[10] A. Canino, On p-convex Sets and Geodesics, J. Diff. Eq., Vol. 75, 1988, pp. 118-157. | MR 957011 | Zbl 0661.34042

[11] G. Galloway, Closed Timelike Geodesics, Trans. Am. Math. Soc., Vol. 285, 1984, pp. 379-388. | MR 748844 | Zbl 0547.53033

[12] G. Galloway, Compact Lorentzian Manifolds Without Closed Nonspacelike Geodesics, Proc. Am. Math. Soc., Vol. 98, 1986, pp. 119-124. | MR 848888 | Zbl 0601.53053

[13] C. Greco, Periodic Trajectories for a Class of Lorentz Metrics of a Time-Dependent Gravitational Field, preprint, Dip. Mat. Univ. Bari, 1989. | MR 1060690

[14] C. Greco, Periodic Trajectories in Static Space-Times, preprint, Dip. Mat. Univ. Bari, 1989. | MR 1025457

[15] S.W. Hawking and G.F. Ellis, The Large Scale Structure of Space Time, Cambridge Univ. Press, 1973. | MR 424186 | Zbl 0265.53054

[16] J. Milnor, Morse Theory, Ann. Math. Studies, Vol. 51, Princeton Univ. Press, 1963. | Zbl 0108.10401

[17] J. Nash, The Embedding Problem for Riemannian Manifolds, Ann. Math., Vol. 63, 1956, pp. 20-63. | MR 75639 | Zbl 0070.38603

[18] B. O'Neil, Semi-Riemannian Geometry with Applications to relativity, Academic Press Inc., New York-London, 1983. | Zbl 0531.53051

[19] R.S. Palais, Critical Point Theory and the Minimax Principle, Global Anal., Proc. Sym. "Pure Math.", Vol. 15, Amer. Math. Soc., 1970, pp. 185-202. | MR 264712 | Zbl 0212.28902

[20] R.S. Palais, Morse Theory on Hilbert Manifolds, Topology, Vol. 22, 1963, pp. 299- 340. | MR 158410 | Zbl 0122.10702

[21] R. Penrose, Techniques of Differential Topology in Relativity, Conf. Board Math. Sci., Vol. 7, S.I.A.M., Philadelphia, 1972. | MR 469146 | Zbl 0321.53001

[22] P.H. Rabinovitz, Minimax Methods in Critical Point Theory with Applications to Differential Equations, Reg. Conf. Series, Am. Math. Soc., Vol. 65, 1986. | MR 845785 | Zbl 0609.58002

[23] J.T. Schwartz, Nonlinear Functional Analysis, Gordon and Breach, New York, 1969. | MR 433481 | Zbl 0203.14501

[24] H.J. Seifert, Global Connectivity by Time-Like Geodesics, Z. Natureforsch, Vol. 22 a, 1970, pp. 1356-1360. | MR 225556 | Zbl 0163.43701

[25] J.P. Serre, Homologie singulière des espaces fibres, Ann. Math., Vol. 54, 1951, pp. 425- 505. | MR 45386 | Zbl 0045.26003

[26] F. Tripler, Existence of Closed Time-Like Geodesics in Lorentz Spaces, Proc. Am. Math. Soc., Vol. 76, 1979, pp. 145-147. | Zbl 0387.53024

[27] K. Uhlenbeck, A Morse Theory for Geodesics on a Lorentz Manifold, Topology, Vol. 14, 1975, pp. 69-90. | MR 383461 | Zbl 0323.58010

[28] M. Vigue-Poirier and D. Sullivan, The Homology Theory of the Closed Geodesic Problem, J. Diff. Geom., Vol. 11, 1979, pp. 633-644. | MR 455028 | Zbl 0361.53058