Take the 2-minute tour ×

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?

share|improve this question
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 1

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.

share|improve this answer
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

Your Answer


