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Multiplicity of Timelike Geodesics in Splitting Lorentzian Manifolds

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Recent Developments in General Relativity
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Abstract

In the theory of General Relativity models of gravitational fields are particular examples of Lorentzian manifolds, the so-called space-times, and the trajectory of a free falling particle on which only gravity acts is just a timelike geodesic in such a manifold [1,2].

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References

  1. Beem J.K., Ehrlich P.E., Easley K.L. (1996): Global Lorentzian Geometry. Monographs Textbooks Pure Appl. Math. 202, Dekker, New York

    MATH  Google Scholar 

  2. Hawking S.W., Ellis G.F.R. (1973): The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge

    Book  MATH  Google Scholar 

  3. Candela A.M., Giannoni F., Masiello A.: Multiple critical points for indefinite functionals and applications. J. Differential Equations, to appear

    Google Scholar 

  4. O’Neill B. (1983): Semi-Riemannian Geometry with Applications to Relativity. Academic Press Inc., New York

    MATH  Google Scholar 

  5. Greco C. (1990): Periodic trajectories for a class of Lorentz metrics of a time-dependent gravitational field. Math. Ann. 287, 515–521

    Article  MathSciNet  MATH  Google Scholar 

  6. Masiello A. (1995): On the existence of a timelike trajectory for a Lorentzian metric. Proc. Roy. Soc. Edinburgh A 125, 807–815

    Article  MathSciNet  MATH  Google Scholar 

  7. Candela A.M., Masiello A., Salvatore A.: Existence and multiplicity of normal geodesies in Lorentzian manifolds. J. Geom. Anal, to appear

    Google Scholar 

  8. Benci V., Fortunato D., Masiello A. (1994): On the geodesic connectedness of Lorentzian manifolds. Math. Z. 217, 73–93

    Article  MathSciNet  MATH  Google Scholar 

  9. Giannoni F, Masiello A. (1995): Geodesies on product Lorentzian manifolds. Ann. Inst. H. Poincaré Anal. Non Linéaire 12, 27–60

    MathSciNet  MATH  Google Scholar 

  10. Masiello A. (1994): Variational Methods in Lorentzian Geometry. Pitman Res. Notes Math. Ser. 309, Longman Sci. Tech., Harlow

    Google Scholar 

  11. Klingenberg W. (1978): Lectures on Closed Geodesies. Springer, Berlin

    Book  Google Scholar 

  12. Klingenberg W. (1982) Riemannian Geometry, de Gruyter, Berlin

    MATH  Google Scholar 

  13. Fadell E. (1985): Lectures in cohomological index theories of G-spaces with applications to critical point theory. Raccolta di seminari, Università della Calabria

    Google Scholar 

  14. Fournier G., Willem M. (1990): Relative category and the calculus of variations, in Variational problems, ed. by H. Beresticky, J.M. Coron, I. Ekeland, Birkhäuser, Basel, pp. 95–104

    Google Scholar 

  15. Szulkin A. (1990): A relative category and applications to critical point theory for strongly indefinite functionals, Nonlinear Anal. TMA 15, 725–739

    MathSciNet  MATH  Google Scholar 

  16. Palais R.S. (1966): Lusternik-Schnirelman theory on Banach manifolds. Topology 5, 115–132

    Article  MathSciNet  MATH  Google Scholar 

  17. Fadell E., Husseini S. (1991 ): Category of loop spaces of open subsets in Euclidean space. Nonlinear Anal. TMA 17, 1153–1161

    Article  MathSciNet  MATH  Google Scholar 

  18. Fadell E., Husseini S. (1994): Relative category, products and coproducts. Rend. Sem. Mat. Fis. Univ. Milano LXIV, 99–117

    Article  MathSciNet  Google Scholar 

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© 2000 Springer-Verlag Italia

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Candela, A.M. (2000). Multiplicity of Timelike Geodesics in Splitting Lorentzian Manifolds. In: Casciaro, B., Fortunato, D., Francaviglia, M., Masiello, A. (eds) Recent Developments in General Relativity. Springer, Milano. https://doi.org/10.1007/978-88-470-2113-6_23

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  • DOI: https://doi.org/10.1007/978-88-470-2113-6_23

  • Publisher Name: Springer, Milano

  • Print ISBN: 978-88-470-0068-1

  • Online ISBN: 978-88-470-2113-6

  • eBook Packages: Springer Book Archive

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