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Suppose a body has just enough matter in it that just 1 more electron could turn it into a blackhole. When this happens, where does all that matter go?

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We know where the matter goes because once inside the horizon all timelike paths lead to the singularity at the centre, so all matter falls into the singularity. What we don't know is what happens at the singularity.

We can trace the path followed by infalling matter by integrating the line element $ds$ along the trajectory. The problem is that at the singularity the curvature becomes infinite and it isn't possible to integrate any farther. This is the notorious problem of geodesic incompleteness. It's hoped that some future theory of quantum gravity will remove the singularity and allow us to find out what happens to the matter hitting it.

You should note that for external observers, i.e. those outside the event horizon, the black hole never forms so the matter never goes anywhere. It is only infalling observers who will see anything (i.e. themselves) reach the singularity.

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I've never understood how it can be an external observer will never see the formation of a black hole, yet we see black holes in the universe. When could they have formed? –  Richardbernstein Feb 17 '13 at 18:02
@Richardbernstein: we don't see black holes, we see concentrations of matter so great that we know they must form black holes, even though we will never see them do this. We tend to just call such concentrations of matter "black holes" because it's convenient. –  John Rennie Feb 18 '13 at 7:33

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