An improved formula for the frequency shift due to a variable phase speed

The mathematical problem of linear wave propagation in a medium with slowly spatially-varying phase speed is examined by means of the multiple-scale perturbation technique. Specifically, the propagation of electromagnetic waves in a gravitational field, when the speed of light is a function of the strength of the potential, is considered. A new solution is found, which improves the well-known formula, based on a 'quasi-constant' assumption. The latter is compared to the new expression for the gravitational redshift of light emitted from the surface of a massive body, and it is shown to deviate up to 20% in the region around a few radii from the emitting surface. (fast track communication)