Deflection of Light and Shapiro Delay: An Equivalent Medium Theory Approach

Abstract

We discuss the deflection of light and Shapiro delay under the influence of gravity as described by Schwarzschild metric. We obtain an exact expression based on the coordinate velocity, as first set forth by Einstein, and present a discussion on the effect of velocity anisotropy. We conclude that the anisotropy in the coordinate velocity, as the velocity apparent to a distant observer, gives rise to a third order error in the deflection angle, so that the practical astronomical observations from gravitational lensing data remain inconclusive on the anisotropy. However, measurement of Shapiro delay provides a fairly convenient way to determine whether the spacetime is optically anisotropic for a distant observer or not. We calculate the Shapiro delay for a round trip path between Earth and Venus and observe excellent agreement to two experimentally reported values measured during a time span of six months in 1967, without any need to extra fitting parameters. This is while the expected delay obtained from an isotropic light velocity as described by Einstein's model suffers from much larger errors under similar conditions. This article illustrates the usefulness of the equivalent medium theory in understanding of general theory of relativity.