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We present a framework, based on the null-surface formulation of generalrelativity, for discussing the dynamics of Fermat potentials for gravitationallensing in a generic situation without approximations of any kind.Additionally, we derive two lens equations: one for the case of thick compactlenses and the other one for lensing by gravitational waves. These equations inprinciple generalize the astrophysical scheme for lensing by removing thethin-lens approximation while retaining the weak fields.Comment: Accepted for publication in Phys. Rev.

Dynamics of Fermat potentials in nonperturbative gravitational lensing