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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