Exact Solutions
A table of exact solutions of the Einstein field equations consists of the following:
| Non-rotating | Rotating | |
| Uncharged | Schwarzschild | Kerr |
| Charged | Reissner–Nordström | Kerr–Newman |
The more often used exact equation for gravitational redshift applies to the case outside of a non-rotating, uncharged mass which is spherically symmetric. The equation is:
, where
- is the gravitational constant,
- is the mass of the object creating the gravitational field,
- is the radial coordinate of the point of emission (which is analogous to the classical distance from the center of the object, but is actually a Schwarzschild coordinate),
- is the radial coordinate of the observer (in the formula, this observer is at an infinitely large distance), and
- is the speed of light.
Read more about this topic: Gravitational Redshift
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