Some properties of light propagation in relativity

An outline of a formalism is proposed that describes relativistic effects associated with the propagation of light rays which after being initially split start to reconverge and intersect each other again. Beside a general geometric description that uses the approach of geometric optics, it has been shown how to compute both the difference of the proper times of arrivals of the two light beams to a measuring apparatus, as well as the frequency shifts of each of the beams taken separately. The formalism used here is applicable to both the special and the general theory of relativity, and it can be used equally well either when the light split is, produced by a man-made optical device or when it is caused by the gravity field itself. The geometric description used in the formalism is independent of the physical origin of the frequency shift; of whether it is a Doppler, gravitational or cosmological frequency shift effect. Two simple examples of the application of the formalism have been worked out, which illustrate its results for families of inertial and noninertial observers respectively. Furthermore, a short description of a continuous version of the formalism has been presented in the last section of the article.