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Originally Posted by publius
Grant,
There is an indeed an exact solution of a "point mass" against a deSitter (lambda, expanding universe) background, one metric called oddly enough the Schwarzschild-deSitter (SdS) metric.
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The important question in the context of this discussion is, I think, whether this metric is actually applicable to objects as strongly bound as planetary systems and galaxies, or if it finds its usefulness only at the scale of clusters and superclusters. I'm not suggesting I know the answer
. But Rindler, in his
Relativity: Special, General, and Cosmological (his second comma, not mine!) seems to come down quite firmly for a non-expanding metric at the planetary scale.
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... the observed expansion is no more mysterious than the flying apart of shrapnel from a grenade that explodes in mid-air. And this image also answers the question whether everything must expand. If two shrapnel pieces could briefly reach out and hold hands to halt their relative motion, they would henceforth be quite unaffected by the motion of the rest. It is much the same in the universe: the forces holding atoms and molecules together have decoupled their constituents from the general expansion; the gravity that holds the stars in a galaxy together has decoupled them from the expansion. We have already seen (in Birkhoff's theorem) that the Schwarzschild metric (and with it the planetary orbits) is unaffected by the existence of expanding surrounding mass shells. The local situation in the universe is quite analogous.
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Grant Hutchison