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Birkhoff's theorem proves qualities about general relativity that demonstrate its relation to Newtonian gravity, i.e., conditions under which the two converge. One consequence is that under GR, isolated, non-rotating, spherically-symmetric masses are equivalent to gravity from a point mass, analogous to what Isaac Newton proved regarding Newtonian gravity to make it practical to apply it to the dynamics of the solar system. A corollary to this is that a spherically symmetric pulsation (e.g., a star's pulsation that happens to retain perfect spherical symmetry of its mass) creates no gravitational waves.
Note that a number of Birkhoff's other widely-known theorems are each also often referred to as Birkhoff's theorem.