In physics, Birkhoff's theorem in electromagnetism, attributed to George D. Birkhoff, concerns spherically symmetric solutions of the source-free Maxwell equations and states that any such solution must be static. Pappas gave two independent proofs of the result in 1984, one directly from Maxwell's equations and one using Lie derivatives, and the theorem is understood as the flat-spacetime, no-backreaction limiting case of the better-known Birkhoff's theorem of general relativity.
Facts
StatementAny spherically symmetric solution of the source-free Maxwell equations is necessarily static. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source Wolfram MathWorld: Birkhoff's Theorem (General Relativity)
Proved By
Source Birkhoff's theorem (electromagnetism) (Wikipedia)
Sources
1. Birkhoff's theorem (electromagnetism) (Wikipedia)
Introduction
any spherically symmetric solution of the source-free Maxwell equations is necessarily static
Lead section
Pappas (1984) gives two proofs of this theorem, using Maxwell's equations and Lie derivatives.
Proved By: George David Birkhoff, Lead
The theorem is due to George D. Birkhoff.
View the SourceWolfram MathWorld: Birkhoff's Theorem (General Relativity)
Wolfram MathWorldIn Branch: Algebraic Geometry, Subject classificationsQuote, In Branch: Algebraic Geometry, Subject classifications
Algebra Algebraic Geometry
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