Fermat principle in arbitrary gravitational fields

The Fermat principle is reviewed and used to derive the zigzag path constructed for massive and massless particles in order to determine if these paths are a suitable approximation to the first order of the gravitational lens effect. It is found that such paths are suitable for thin comoving gravitational lenses to the first order in the lens effect, and also if there is a nonstationary perturbation. As an example, the Fermat principle is applied to a perturbation by gravitational waves, and the transverse velocity of the caustic motion is derived. This velocity creates difficulty for the proposal by McBreen and Metcalfe (1988) that gamma-ray bursts come from small, hot BL Lac cores crossed by microcaustics.