The optical-mechanical analogy in general relativity: Exact Newtonian forms for the equations of motion of particles and photons
If, in a static spacetime, the spatial part of the metric is conformally flat, the effect of the gravitational field on (vacuum) light rays can be mimicked by an optical medium with an effective index of refraction. Correspondingly, those light rays are characterized by a variational principle that is completely analogous to the elementary optics textbook version of Fermat's principle. In the paper under review, the authors revisit this well-known analogy and its generalization to the case of massive particles. Several applications are indicated, in particular the motion of light rays and particles in a Reissner-Nordström type metric is considered in some detail.
scientific article; zbMATH DE number 887105
scientific article