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

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SUMMARY

The gravitational redshift formula is defined as frequency2 = function(frequency1, radius1, radius2, gravitating_mass). The redshift factors combine multiplicatively, allowing the calculation of the redshift between two radii by dividing the known redshift at infinity. Additionally, the time derivative of frequency during the ascent of a photon is a key aspect of this discussion, emphasizing the need for a precise mathematical representation of these concepts.

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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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