Abstract
We present a variational principle, similar to the Fermat principle in Optic, concerning the existence of lightlike geodesies joining two submanifolds in stationary Lorentzian manifolds.
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References
Giannoni F., Masiello A., Piccione P. (1997): A variational theory for light rays in stably causal Lorentzian manifolds. Existence and regularity results. Comm. Math. Phys. 187, 375–415
Giannoni F., Masiello A., Piccione P. (1998): A Morse theory for light rays on stably causal Lorentzian manifolds. Ann. Inst. H. Poincaré, Physique thèorique 69, 359–412
Masiello A., Piccione P. (1998): Shortening null geodesies in Lorentzian manifolds. Applications to closed light rays. Differential Geom. Appl. 8, 47–70
Fortunato D., Masiello A. (1995): Fermat Principles in General Relativity and the Existence of Light Rays on Lorentzian Manifolds, in Proc. Variational and Local Methods in the Study of Hamiltonian Systems ICTP, ed. by A. Ambrosetti, G.F. Dell’Antonio, World Scientific, Singapore, pp. 34–64
Hawking S.W., Ellis G.ER. (1973): The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge
Fortunato D., Giannoni F., Masiello A. (1995): A Fermat principle for stationary space times and applications to light rays. J. Geom. Phys. 15, 159–188
Molina J. (1996): Existence and multiplicity of normal geodesies on static space-time manifolds. Bull. Un. Mat. Ital. A 10, 305–318
Candela A.M. (1996): Lightlike periodic trajectories in space-times. Ann. Mat. PuraAppl. CLXXI, 131–158
Candela A.M., Salvatore A. (1997): Light rays joining two submanifolds in space-times. J. Geom. Phys. 22, 281–297
Grove K. (1973): Condition (C) for the energy integral on certain path spaces and applications to the theory of geodesies. J. Differential Geom. 8, 207–223
Salvatore A. (1996): Trajectories of dynamical systems joining two given submanifolds. Differential Integral Equations 9, 779–790
Klingenberg W. (1982): Riemannian Geometry, de Gruyter, Berlin
Giannoni F., Masiello A. (1991): On the existence of geodesies on stationary Lorentz manifolds with convex boundary. J. Funct. Anal. 101, 340–369
Schwartz J.T. (1969): Nonlinear Functional Analysis. Gordon and Breach, New York
Fadell E., Husseini S. (1991): Category of loop spaces of open subsets in Euclidean space. Nonlinear Anal. TMA 17, 1153–1161
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Salvatore, A. (2000). Null Geodesics Joining Two Submanifolds in Stationary 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_28
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DOI: https://doi.org/10.1007/978-88-470-2113-6_28
Publisher Name: Springer, Milano
Print ISBN: 978-88-470-0068-1
Online ISBN: 978-88-470-2113-6
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