# The Black Hole Problem

Consider a spherical body of uniform density $\rho$ and initial radius R. You can imagine this body containing another sphere of radius R/2 which touches the center and the periphery of the larger sphere. The smaller sphere has 8 times less mass, since the mass goes as the radius cubed.

If you let the big sphere collapse gravitationally along with the smaller one, keeping the density uniform, the whole thing just shrinks proportionally. The Schwarzschild radius is proportional to the mass, so $R_S= 2GM/c^2$ for the larger mass, and for the smaller sphere $r_S= 2GM/8c^2$, one eigth as big. So when the large mass collapses, the smaller one hasn’t.

It follows that the smaller sphere can still communicate with things outside, but the larger sphere should prevent it from doing so. The outgoing world lines at P due to the smaller sphere must be trapped by the spacetime effects of the residual portion ie, the portion represented by the larger sphere minus the smaller one.It seems that the remaining larger irregular shaped mass has a greater attractive power than the regular shape of greater mass at specific points like P.Is it really so?

For a sphere of a larger fraction of the size, say 3/5R, which touches the boundary of the larger sphere at some point and includes the center [of the larger sphere, the smaller Schwarzschild radius is about .2 of the larger Schwarzschild radius.

When the larger sphere collapses the smaller one has not collapsed---it has world lines in the outward direction.The smaller sphere is not supposed to have a singularity on its own.But it contains the singularity of the bigger mass , though not at its center.Is the singularity, [of the larger sphere], produced by the effect of the residual portion?

Related question: Can we conclude solely on the basis of these “Experiments’ that different parts of the body can exchange signals after it has collapsed? [QM effects are not being considered in this problem]

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You don't need to go into such detail--- you can just say it as I edited it. If you don't like it, feel free to roll back. – Ron Maimon May 10 '12 at 7:53
You have asked 17 questions and marked none as accepted. Worse, you haven't voted on any answers to your questions! This is very bad manners. Please see physics.stackexchange.com/faq#howtoask – Mark S. Everitt May 10 '12 at 8:47
Einstein field equation is non-linear. It makes no sense to say "attraction" due to specific part as in Newtonian gravity. – C.R. Jul 9 '12 at 10:17

 "As the collapse happens, everything is squeezed down $nonuniformly$ with the bound provided by the collapsing light-cone"----Ron Maimon. The Schwarzschild metric,incidentally, is a spherically metric. Is it consistent with any type of non-uniformity in side the mass? – Anamitra Palit May 10 '12 at 8:51 @AnamitraPalit: nonuniform in r, still rotational invariant. – Ron Maimon May 10 '12 at 17:25