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arXiv · 1307.3291

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

Valeri P. Frolov
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Abstract

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.

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Valeri P. Frolov. 2013-07-11. Generalized Fermat's principle and action for light rays in a curved spacetime. https://doi.org/10.1103/physrevd.88.064039

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