Continuing on the PF2 thread about singularities... I had a thought that might give a sort of intuitive explanation of the singularity theorems -- eg the proofs that singularities exist at the center of black holes: Remember how photons emitted just exactly at the edge of black hole are supposed to be 'trapped' there and not moving at all? Now, how do we reconcile this with the relativity notion of light always going at c? Well, in a frame right next to the edge of the black hole, you see the event horizon itself expanding at almost the speed of light -- run as you can, you can't escape it. The intuitive picture this leads to is that the black hole is sort of "sucking" spacetime itself into it. The effect of curvature->pulling matter together->more curvature goes into a feedback loop, and the spacetime fabric pulls the matter into a singularity. A better way to put it: in a black hole, the curvature of spacetime -- the rate at which distances shrink -- becomes greater than the speed of light. Since particles can't move faster than this, it doesn't matter what forces or accelerations they feel; spacetime 'wins' and keeps pushing them closer together. From what I know of GR and have read of the singularity thms, this seems to be the intuitive/heuristic explanation of what the field equations actually say happens. I think.... does this help anyone?