Birkhoff's theorem (relativity)

General relativity
${\displaystyle G_{\mu \nu }+\Lambda g_{\mu \nu }={\kappa }T_{\mu \nu }}$
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The theorem was proven in 1923 by George David Birkhoff (author of another famous Birkhoff theorem, the pointwise ergodic theorem which lies at the foundation of ergodic theory). In 2005, Nils Voje Johansen, Finn Ravndal, Stanley Deser^{[citation needed]} stated that the theorem was allegedly published two years earlier by a little-known Norwegian physicist, Jørg Tofte Jebsen.^{[5][6][non-primary source needed][original research?]}

Intuitive rationale

The intuitive idea of Birkhoff's theorem is that a spherically symmetric gravitational field should be produced by some massive object at the origin; if there were another concentration of

Generalizations

Birkhoff's theorem can be generalized: any spherically symmetric and asymptotically flat solution of the

Einstein/Maxwell field equations

, without ${\displaystyle \Lambda }$, must be static, so the exterior geometry of a spherically symmetric charged star must be given by the

See also

• Birkhoff's theorem (electromagnetism)
• Newman–Janis algorithm, a complexification technique for finding exact solutions to the Einstein field equations
• Shell theorem in Newtonian gravity
• Quadrupole formula

References