We define a variational problem based on the arrival time functional for timelike curves on a Lorentzian manifold M parameterized by a fixed constant multiple of their proper time. Under a causality assumption for the manifold M, we prove that the stationary points of our problem are geodesics, obtaining an extension of the Fermat's Principle for light rays proven in [14] (see also [2]). Moreover, we study the compactness properties of the arrival time functional by global variational techniques. Under intrinsic assumptions on the metric of M we get results of existence and multiplicity for geodesics with a given energy between an event and an observer of M.

A timelike extension of Fermat's principle in general relativity and applications / Giannoni, F.; Masiello, A.; Piccione, P.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 6:3(1998), pp. 263-283. [10.1007/s005260050091]

A timelike extension of Fermat's principle in general relativity and applications

Masiello, A.;
1998-01-01

Abstract

We define a variational problem based on the arrival time functional for timelike curves on a Lorentzian manifold M parameterized by a fixed constant multiple of their proper time. Under a causality assumption for the manifold M, we prove that the stationary points of our problem are geodesics, obtaining an extension of the Fermat's Principle for light rays proven in [14] (see also [2]). Moreover, we study the compactness properties of the arrival time functional by global variational techniques. Under intrinsic assumptions on the metric of M we get results of existence and multiplicity for geodesics with a given energy between an event and an observer of M.
1998
A timelike extension of Fermat's principle in general relativity and applications / Giannoni, F.; Masiello, A.; Piccione, P.. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - STAMPA. - 6:3(1998), pp. 263-283. [10.1007/s005260050091]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11589/10170
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