2005/08/08 by Volker Perlick · 94 citations
Physics and Astronomy · #Advanced Differential Geometry Research #Astrophysics and Cosmic Phenomena #Classical mechanics #Closed timelike curve #Cosmology and Gravitation Theories #Curvature #Differential geometry #Finsler manifold #Geodesic #Geometry #Manifold (fluid mechanics) #Mathematical analysis #Mathematical physics #Metric (unit) #Physics #Quantum #Quantum field theory in curved spacetime #Quantum gravity #Quantum mechanics #Spacetime #Stationary spacetime #Variational principle #gr-qc
paper · pdf · doi:10.1007/s10714-005-0225-6
published in General Relativity and Gravitation 38(2), 365-380 (Springer Science+Business Media) · 18 pages, submitted to Gen. Rel. Grav
arxiv created 2005/08/08 · openalex publication_date 2006/01/18 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
It is shown that, on a manifold with a Finsler metric of Lorentzian signature, the lightlike geodesics satisfy the following variational principle. Among all lightlike curves from a point (emission event) to a timelike curve (worldline of receiver), the lightlike geodesics make the arrival time stationary. Here ``arrival time'' refers to a parametrization of the timelike curve. This variational principle can be applied (i) to the vacuum light rays in an alternative spacetime theory, based on Finsler geometry, and (ii) to light rays in an anisotropic non-dispersive medium with a general-relativistic spacetime as background.