**Gravitational Redshift**

In the theory of general relativity, there is time dilation within a gravitational well. This is known as the gravitational redshift or *Einstein Shift*. The theoretical derivation of this effect follows from the Schwarzschild solution of the Einstein equations which yields the following formula for redshift associated with a photon traveling in the gravitational field of an uncharged, nonrotating, spherically symmetric mass:

where

- is the gravitational constant,
- is the mass of the object creating the gravitational field,
- is the radial coordinate of the source (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate), and
- is the speed of light.

This gravitational redshift result can be derived from the assumptions of special relativity and the equivalence principle; the full theory of general relativity is not required.

The effect is very small but measurable on Earth using the Mössbauer effect and was first observed in the Pound-Rebka experiment. However, it is significant near a black hole, and as an object approaches the event horizon the red shift becomes infinite. It is also the dominant cause of large angular-scale temperature fluctuations in the cosmic microwave background radiation (see Sachs-Wolfe effect).

Read more about this topic: Red Shift, Redshift Formulae

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