I understand that, as matter approaches the event horizon of a black hole, according to the time frame of someone outside the black hole, it would slow down and, after an infinite time, stop completely at the event horizon. So, if we could observe it, all this matter would be accumulating just outside the event horizon rather than passing through it. This might suggest that the matter that forms a black hole is in a thin shell near the event horizon rather than at a singularity in the centre. Is this the case or have I missed something? As more matter arrives, the black hole would presumably grow and the event horizon would move outwards, thus engulfing the matter rather than the matter 'falling' in. Would the matter then proceed to the singularity? I suspect maybe not: I have heard it suggested that time is reversed inside the event horizon. If that is the case, might the matter inside then move back outwards towards the event horizon, thus still preserving the thin shell?