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
Famous quotes containing the words exact and/or solutions:
“Neither Aristotelian nor Russellian rules give the exact logic of any expression of ordinary language; for ordinary language has no exact logic.”
—Sir Peter Frederick Strawson (b. 1919)
“Science fiction writers foresee the inevitable, and although problems and catastrophes may be inevitable, solutions are not.”
—Isaac Asimov (1920–1992)