Gravitation Redshift for very dense stars

[Rubber Ducky]

Homework Statement

In deriving the expression $\frac{f'-f}{f}=\frac{gH}{c^2}=\frac{GM_s}{R_sc^2}$ , it was assumed that $\triangle f=f'-f$ was small, and that the photon had a constant mass of $\frac{hf}{c^2}$. Suppose that a star is so dense that $\triangle f$ is not small.

(a) Show that $f'$, the photon frequency at $\infty$, is related to $f$, the photon frequency at the star's surface, by $f'=fe^{-GM_s/R_sc^2}$

(b) Show that (a) reduces to $f'=f(1-\frac{GM_s}{R_sc^2})$ for small $M_s/R_s$

Homework Equations

I believe all of the important ones were listed in the problem statement. I apologize if I missed some.

The Attempt at a Solution

I really have no idea where to start. The exponential in (a) seems to pop out of nowhere.

 

[Greg Bernhardt]

Thanks for the post! Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?