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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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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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