# Gravitation Redshift for very dense stars

1. Oct 14, 2014

### Rubber Ducky

1. The problem statement, all variables and given/known data
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 $M_s/R_s$

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

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

2. Oct 20, 2014