1307.3291 (Valeri P. Frolov)

Generalized Fermat's principle and action for light rays in a curved
spacetime    [PDF]

Valeri P. Frolov

We start with formulation of the generalized Fermat's principle for light propagation in a curved spacetime. We apply Pontryagin's minimum principle of the optimal control theory and obtain an effective Hamiltonian for null geodesics in a curved spacetime. We explicitly demonstrate that dynamical equations for this Hamiltonian correctly reproduce null geodesic equations. Other forms of the action for light rays in a curved spacetime are also discussed.

View original: http://arxiv.org/abs/1307.3291