THE OPTICAL-MECHANICAL ANALOGY IN GENERAL-RELATIVITY - EXACT NEWTONIAN FORMS FOR THE EQUATIONS OF MOTION OF PARTICLES AND PHOTONS

In many metrics of physical interest, the gravitational field can be r ep resented as an optical medium with an effective index of refraction . We show that, in such a metric, the orbits of both massive and massl ess particles are governed by a Variational principle which involves t he index of refraction and which assumes the form of Fermat's principl e or of Maupertuis's principle. From this variational principle we der ive exact equations of motion of Newtonian form which govern both mass less and massive particles. These equations of motion are applied to s ome problems of physical interest.