An optical perspective on the theory of relativity - II: Gravitational deflection of light and Shapiro time delay

Abstract

By regarding a gravitational field as a special optical medium, we define its refractive index using the general form of the solution to the Einstein equation in general relativity. A generalized version of Snell's law is given by comparing the space structure of a gravitational field with that of optical medium. The applicability of Snell's law is extended from Euclidean space to a spherical symmetrical gravitational field space. Drawing upon the generalized version of Snell's law, geometrical optics are used to arrive at formulas for the gravitational deflection of light and Shapiro time delay in a spherically symmetric gravitational field. These formulas are identical to those obtained by using geodesic equations in general relativity, thus proving that a gravitational field is a special optical medium.