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.
Facts
Partially Attested
Proof YearFirst proven by Jebsen in 1921 and rediscovered by Birkhoff in 1923; 1921 given as the first proof. StatementAny spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Sources
1. Birkhoff's theorem (relativity) (Wikipedia)
Statement of the theorem
any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat
History
The theorem was first proven by Jørg Tofte Jebsen in 1921 and rediscovered in 1923 by George David Birkhoff
View the SourceReader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.