Fermat's Principle in General Relativity via Herglotz Variational Formalism

Abstract

New form of Fermat's principle for light propagation in arbitrary (i.e. in general neither static nor stationary) gravitational field is proposed. It is based on Herglotz extension of canonical formalism and simple relation between the dynamics described by the Lagrangians homogeneous in velocities and the reduced dynamics on lower-dimensional configuration manifold. This approach is more flexible as it allows to extend immediately the Fermat principle to the case of massive particles and to eliminate any space-time coordinate, not only $x^0$.

27 pages, 1 figure, the title changed, considerably extended version

References in corpus (7)

• The Jacobi-metric for timelike geodesics in static spacetimes
• From an Action Principle for Action-dependent Lagrangians toward non-conservative Gravity: accelerating Universe without dark energy
• An Action Principle for Action-dependent Lagrangians: toward an Action Principle to non-conservative systems
• Noether theorem for action-dependent Lagrangian functions: conservation laws for non-conservative systems
• A New Action for Cosmology
• Generalized Fermat's principle and action for light rays in a curved spacetime
• Herglotz Action for Homogeneous Cosmology

Cited by in corpus (1)

• Coupling constant metamorphosis, Fermat principle and light propagation in Kerr metric