Birkhoff's theorem

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This term Birkhoff's theorem is used for several theorems fundamental to different areas of mathematics and physics:

• The ergodic theorem of George David Birkhoff relates averages over time and space; see ergodic theory.

• The HSP theorem of Garrett Birkhoff characterises varieties of algebraic structures; see variety (universal algebra).

• The representation theorem for distributive lattices of Garrett Birkhoff establishes a bijection between finite posets and finite distributive lattices; see distributive lattice.

• The Birkhoff theorem of relativity, proved in 1923 by George David Birkhoff, shows that the most general spherically symmetric solution of the vacuum Einstein equation is the Schwarzschild solution. A discussion of Birkhoff's theorem may be found in Birkhoff's theorem (relativity).

• The Birkhoff theorem in electromagnetism states that a spherically symmetric solution to the source-free Maxwell's equations is static. A discussion of this theorem may be found in Birkhoff's theorem (electromagnetism).