What is the formula for gravitational redshift and its time derivative?

birulami
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Gravitational redshift formula

Hi,

I am looking for the formula that describes the gravitational redshift as

frequency2 = function(frequency1, radius1, radius2, gravitating_mass)

What I find on the net is http://www.wolframalpha.com/input/?i=gravitational+redshift+from+r1+to+r2" the redshift factor for radius2 being infinity. I don't see how I easily compute a 2nd frequency from a first and from a delta distance.

Anyone know the formula?
 
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The redshifts simply combine multiplicatively. Therefore if you know the redshift at infinity you can find the redshift between r1 and r2 by division.
 


In extension of my original post, I would actually like to have the time derivative of the frequency as the photon climbs up.

Anyone?
 
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