# Does gravitation of a sphere equal gravitation of a point?

Under Newtonian model of gravity, a perfect sphere creates the same gravitation field as a point mass in its center.

General Relativity describes gravitation differently. How much this difference affect the above equivalence? If it does not hold, what kind of difference (qualitatively) there is?

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Are you familiar with Birkhoff's Theorem? See en.wikipedia.org/wiki/Birkhoff%27s_theorem_%28relativity%29 – Qmechanic Jun 12 '11 at 20:20
I wasn't, else I'd not be asking :) But thanks for the right cue. – 9000 Jun 12 '11 at 22:38

## 1 Answer

Actually, the same result is true in general relativity: any spherically symmetric mass distribution gravitates in exactly the same way as a point mass.

Here's the more precise statement: any spherically symmetric spacetime, in which all of the matter is concentrated within some radius (i.e., in which the stress-energy tensor vanishes outside of a certain radius), has the same geometry, outside of that radius,as the Schwarzschild metric.

This result is known as Birkhoff's theorem.

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Unless you are inside the sphere. – ja72 Jun 12 '11 at 23:37
@ja72: I don't think Newtonian mechanics consider a sphere a point mass if you're inside the sphere either. – Billy ONeal Jun 13 '11 at 2:18