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On the existence of a timelike trajectory for a Lorentzian metric

Published online by Cambridge University Press:  14 November 2011

Antonio Masiello
Antonio Masiello
Affiliation:
Dipartimento di Matematica, Politecnico di Bari, Via E. Orabona 4, 70125 Bari, Italy
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Abstract

We show the existence of a timelike periodic trajectory for a time-dependent Lorentzian metric on ℝn × ℝ.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 125 , Issue 4 , 1995 , pp. 807 - 815
Copyright
Copyright © Royal Society of Edinburgh 1995

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References

1Benci, V. and Fortunato, D.. Periodic trajectories for the Lorentz metric of a static gravitational field. In Proceedings of ‘Variational Problems’, eds. Berestycki, H., Coron, J. M. and Ekeland, I., pp. 413–29 (Basel: Birkhäuser, 1990).Google Scholar
2Benci, V., Fortunato, D. and Giannoni, F.. On the existence of multiple geodesies in static space-times. Ann. Inst. H. Poincaré, Anal. Non Linéaire 8 (1990), 24–46.Google Scholar
3Benci, V., Fortunato, D. and Giannoni, F.. On the existence of periodic trajectories in static Lorentz manifolds with nonsmooth boundary. In Nonlinear analysis, a Tribute in honour of Giovanni Prodi, pp. 109–33 (Pisa: Quaderni Scuola Normale Superiore, 1991).Google Scholar
4Greco, C.. Periodic trajectories in static space-times. Proc. Roy. Soc. Edingurgh Sect. A 113 (1989), 99–103.CrossRefGoogle Scholar
5Greco, C.. Periodic trajectories for a class of Lorentz-metric of a time-dependent gravitational field. Math. Anal. 287 (1990), 515–21.CrossRefGoogle Scholar
6Greco, C.. Multiple periodic trajectories on stationary space-times. Ann. Mat. Pura Appl. (IV) 162 (1993), 337–48.CrossRefGoogle Scholar
7Klingenberg, W.. Lecture on Closed Geodesies, Grundlehren der Mathematischen Wissenschaften 230 (Berlin: Springer, 1978).CrossRefGoogle Scholar
8Masiello, A.. Time-like periodic trajectories in stationary Lorentz manifolds. Nonlinear Anal. 19 (1992), 531–45.CrossRefGoogle Scholar
9Masiello, A. and Pisani, L.. Existence of a time-like periodic trajectory for a time-dependent Lorentz metric. Ann. Univ. Ferrara Sez. VII 36 (1990), 207–22.CrossRefGoogle Scholar
10Mawhin, J. and Willem, M.. Critical Point Theorems and Hamiltonian Systems (Berlin: Springer, 1989).CrossRefGoogle Scholar
11O'Neill, B.. Semi-Riemannian Geometry with Applications to Relativity, Pure and Applied Mathematics 103 (New York: Academic Press, 1983).Google Scholar
12Rabinowitz, P. H.. MinMax Methods in Critical Point Theory with Applications to Differential Equations, CBMS Regional Conference Series in Mathematics 65 (Providence, RI: American Mathematical Society, 1984).Google Scholar