Fr.: théorème de Birkhoff
For a four dimensional → space-time, the → Schwarzschild metric is the only solution of → Einstein's field equations which describes the gravitational field created by a spherically symmetrical distribution of mass. The theorem implies that the gravitational field outside a sphere is necessarily static, and that the metric inside a spherical shell of matter is necessarily flat.
The theorem was first demonstrated in 1923 by George David Birkhoff (1884-1944), an American mathematician; → theorem