Fermat Principle in Arbitrary Gravitational Fields
Abstract
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 gammaray bursts come from small, hot BL Lac cores crossed by microcaustics.
 Publication:

The Astrophysical Journal
 Pub Date:
 March 1990
 DOI:
 10.1086/168450
 Bibcode:
 1990ApJ...351..114K
 Keywords:

 Fermat Principle;
 Gravitational Fields;
 Gravitational Lenses;
 Doppler Effect;
 Gamma Ray Bursts;
 Gravitational Waves;
 Perturbation Theory;
 Astrophysics;
 GAMMA RAYS: BURSTS;
 GRAVITATION;
 GRAVITATIONAL LENSES;
 RELATIVITY