- #1
Rubber Ducky
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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.