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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
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I wasn't, else I'd not be asking :) But thanks for the right cue. –  9000 Jun 12 '11 at 22:38
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up vote 11 down vote accepted

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
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@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
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