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Black hole formation as seen by a distant observer

Given that matter can never cross the event horizon of a black hole (from an external observer point of view), if a black hole is "fed" with a large amount of matter then the new matter will eventually become extremely compressed, and presumably would be compressed below its Schwarzchild radius.

Would secondary black holes eventually form near the original black hole?

As an alternative one could also imagine that the combined mass of the original black hole and the new mass around the event horizon becomes contained within the Schwarzchild radius of both masses, and so a new event horizon forms, "swallowing" the new mass around the edge of the original black hole.

This mechanism would allow black holes to swallow mass in a finite time.
Would this contradict GR predictions?

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marked as duplicate by dmckee Jan 1 '13 at 17:54

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

    
Surely you can see that this is the same question as your earlier one? I'm willing to listen to arguments that I made a mistake in closing that one, but ... please don't post new copies of closed questions. –  dmckee Jan 1 '13 at 17:54
    
Sorry I thought this was a good question and importantly different to the one you closed previously, as it describes a mechanism for BH to grow that I have not seen previously discussed. –  roblev Jan 1 '13 at 18:56
    
plus it gives an answer directly contradicting physics.stackexchange.com/questions/21319/… and this is quite interesting, no? –  roblev Jan 1 '13 at 19:18
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Of course that black holes can swallow and do swallow additional matter and increase their mass in finite time, whatever reasonable coordinates we choose.

Yes, the Schwarzschild radius for the combined system smaller black hole + extra matter ("food") is larger than it is for the original smaller black hole which means that it's enough for the new matter to cross a critical surface that is outside the original event horizon of the smaller black hole. This occurs in finite time, even from the external observer's viewpoint, and the black hole simply grows in size.

It's a routine process we observe at many places. For example, the black hole at the galactic center devours new matter all the time.

Incidentally, there can't exist any "concentric pairs of black holes" solutions to the 3+1-dimensional general relativity. Once we know that it's the empty Schwarzschild metric up to the event horizon (from outside), then it is the black hole and there's no way for the metric to "unbecome" a black hole again. Everything that is inside the event horizon is, by definition, causally disconnected from infinity – it can't escape to infinity again. So if there is a matter that is even "more inside", at an even lower value of $R$, it's clear that it's still inside the black hole in the sense that it can't get to infinity.

So it's impossible to claim that there is a new "island" near the center of the black hole that would be "outside the black hole" again. Such a thing can't happen, it would be a logical oxymoron, almost by the definition of the event horizon.

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Thanks, this all makes complete sense to me... first time I have seen it written down. Why is it so commonly written that it takes infinite time for matter to cross the event horizon of a BH when it seems it is not true? –  roblev Jan 1 '13 at 19:03
    
The time is infinite in the limit when the mass of the infalling object goes to zero and there's nothing else that makes the black hole grow. So the infalling object is just a "probe". –  Luboš Motl Jan 5 '13 at 7:42
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