Birkhoff's Theorem (General Relativity)

Birkhoff's Theorem states that any spherically symmetric solution of the vacuum Einstein field equations must be static and identical, up to a choice of coordinates, to the Schwarzschild solution, even if the mass generating the field is itself pulsating or otherwise changing over time. Named for George David Birkhoff, who proved it in 1923, it is the general-relativistic analogue of the Newtonian shell theorem, and it explains why a spherically symmetric star cannot radiate gravitational waves purely by radial pulsation.