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  (see also ). 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.
|Titolo:||A timelike extension of Fermat's principle in general relativity and applications|
|Data di pubblicazione:||1998|
|Digital Object Identifier (DOI):||10.1007/s005260050091|
|Appare nelle tipologie:||1.1 Articolo in rivista|