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

In summary, the formula for gravitational redshift is frequency2 = function(frequency1, radius1, radius2, gravitating_mass). The redshift factor for radius2 is infinity, but it can be calculated by dividing the redshift at infinity with the redshift between r1 and r2. Additionally, the time derivative of the frequency can be found as the photon climbs up.
  • #1
birulami
155
0
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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  • #2
The redshifts simply combine multiplicatively. Therefore if you know the redshift at infinity you can find the redshift between r1 and r2 by division.
 
  • #3


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

Anyone?
 

What is the gravitational redshift formula?

The gravitational redshift formula is an equation that describes the shift in wavelength of electromagnetic radiation (such as light) as it travels from a region of higher gravitational potential to a region of lower gravitational potential.

What is the significance of the gravitational redshift formula?

The gravitational redshift formula is significant because it is a prediction of Einstein's theory of general relativity. It has been repeatedly confirmed through experiments and observations, and is a crucial component of our understanding of gravity and the behavior of light in the presence of massive objects.

How is the gravitational redshift formula calculated?

The gravitational redshift formula is calculated using the equation: Δλ/λ = GM/Rc^2, where Δλ is the change in wavelength, λ is the original wavelength, G is the gravitational constant, M is the mass of the object causing the gravitational potential, R is the distance from the object, and c is the speed of light.

What factors affect the gravitational redshift?

The gravitational redshift is affected by the mass of the object causing the gravitational potential, the distance from the object, and the speed of light. Additionally, the redshift will be greater in regions with stronger gravitational fields, such as near black holes.

Can the gravitational redshift formula be applied to other forms of radiation?

Yes, the gravitational redshift formula can be applied to any form of electromagnetic radiation, including radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays. It also applies to gravitational waves, which are ripples in the fabric of spacetime predicted by general relativity.

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