Birkhoff's theorem


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Birkhoff's theorem

[′bərk‚hȯfs ‚thir·əm]
(relativity)
A theorem which states that if a space-time containing matter or energy satisfies Einstein's equations of general relativity and is centrally symmetric, then it is necessarily static and under a coordinate transformation it becomes identical to the Schwarzschild solution.
References in periodicals archive ?
According to Birkhoff's theorem, this solution is also valid for any spherically symmetric body at a distance larger than its radius [2].
According to Birkhoff's theorem, outside the radius R of the collapsing body the space-time geometry will be exactly Schwarzschild-like, so that [phi] = 0 for r > R.
Birkhoff's theorem [1] assures us that for any non-rotating spherically symmetric distribution of matter, the gravitational effect on any test mass is solely due to whatever mass lies closer to the center of symmetry.