Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-26T01:32:53.935Z Has data issue: false hasContentIssue false
  • English
  • Français

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
Get access Rights & Permissions [Opens in a new window]

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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