A Fermat principle on Lorentzian manifolds and applications

DOI10.1016/0893-9659(96)00019-5zbMath0855.53038OpenAlexW2031766299MaRDI QIDQ1921177

Flavia Antonacci, Paolo Piccione

Publication date: 3 February 1997

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0893-9659(96)00019-5

zbMATH Keywords

Lorentz manifoldFermat principlelightlike geodesics

Mathematics Subject Classification ID

Geodesics in global differential geometry (53C22) Global differential geometry of Lorentz manifolds, manifolds with indefinite metrics (53C50) Equations of motion in general relativity and gravitational theory (83C10) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (9)

A timelike extension of Fermat's principle in general relativity and applications ⋮ Shortening null geodesics in Lorentzian manifolds. Applications to closed light rays ⋮ Unnamed Item ⋮ On a morse theory for light rays without nondegeneracy assumptions ⋮ A variational theory for light rays in convex subsets of stably causal lorentzian manifolds ⋮ Global variational methods on a class of nonsmooth nonholonomic constraints ⋮ Light rays having extreme points with the same spatial coordinates ⋮ Existence and multiplicity results for massive particles trajectories in a universe with boundary ⋮ An intrinsic Fermat principle on stationary Lorentzian manifolds and applications.

Cites Work

• A Morse theory for geodesics on a Lorentz manifold
• On Fermat's principle in general relativity. I. The general case
• On Fermat's principle in general relativity. II. The conformally stationary case
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