When we derived the equation for the change in frequency of a photon when moving in a gravitational field, we assumed that the change in frequency was small and that the effective photon mass was constant. Suppose the photon is trying to escape from a star and that it is so dense that the change in frequency is not small.
Show that the photon frequency after it escapes the star, ð‘“′, is given by ð‘“′ = ð‘“ð‘’^(−ðºð‘€/ð‘…ð‘^2), where ð‘“ is the frequency of the photon at the surface of the star, ð‘€ is the mass of the star, and ð‘… is the radius of the star.
Show that the above result reduces to the expression derived in class when ð‘€/ð‘… is small.