Birkhoff's theorem (electromagnetism)

In physics, in the context of electromagnetism, Birkhoff's theorem concerns spherically symmetric static solutions of Maxwell's field equations of electromagnetism.

The theorem is due to George D. Birkhoff. It states that any spherically symmetric solution of the source-free Maxwell equations is necessarily static. Pappas (1984) gives two proofs of this theorem. It is a limiting case of Birkhoff's theorem (relativity) by taking the flat metric without backreaction.

References

• Richard C Pappas, Proof of "Birkhoff's theorem" in electrodynamics, Am. J. Phys., 52 (3) 1984, 255-256.