Birkhoff's theorem in relativity is a theorem pertaining to a particular type of solution of Einstein's field equations of general relativity theory.
More precisely, the theorem says that any spherically symmetric solution of the vacuum field equations is necessarily static. The resulting metric is then the (exterior) Schwarzschild solution. A consequence of Birkhoff's theorem is that a pulsating star that remains spherically symmetric cannot emit gravitational waves.
This is a 1927 result of G. D. Birkhoff.
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