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The no-hair theorem of black holes says they're completely categorised by their charge and angular momentum and mass.

But imagine two black holes colliding. At some point their event horizons would merge and I imagine the combined event horizon would not be spherical.

You could even imagine 50 black holes merging. Then the combined event horizon would be a very odd shape.

Why does this not disprove the no-hair theorem? Since the information about the shape of the event horizon is surely more than just charge, angular momentum and mass?

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No. The no-hair conjecture applies to stable solutions of the Einstein-Maxwell equations. In the case of merging black holes, it applies to the end state of the merger into a single quiescent black hole, after the “ringdown” has stopped.

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    $\begingroup$ It's an odd theorem because most black holes aren't stable, their either evaporating or each particles from the background space. $\endgroup$ – zooby Feb 11 '19 at 0:01
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    $\begingroup$ those processes are slow enough that a black hole that is evaporating or accreting gas (not planets or other big objects) can be considered stable. $\endgroup$ – niels nielsen Feb 11 '19 at 0:09
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    $\begingroup$ Black hole evaporation is a quantum effect. The no-hair conjecture is a conjecture in classical General Relativity since we don’t have any consensus about quantum gravity. Quantum black holes probably do have some kind of hair that encodes all of the information that fell into them. Physicists are trying to figure out how that might work. $\endgroup$ – G. Smith Feb 11 '19 at 0:09
  • $\begingroup$ @zooby or to put the same point another way, it can be seen as a timescale separation. If you assume that the black hole is big enough then it makes sense to ask what the state will look like after a long enough time that all classical transient effects have stopped, but short enough that evaporation isn't significant. (Of course, the no hair theorem is still only a claim about the macroscopic spatial scale in that case - there could still be 'hair' on a microscopic quantum scale that can't be modelled by general relativity alone.) (+1 to both question and answer.) $\endgroup$ – Nathaniel Feb 11 '19 at 7:21
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    $\begingroup$ @G.Smith: Could you tell me if this layman intuition is correct (I'm not a physicist)? My intuition behind the no-hair theorem is that, if everyone agrees on where the event horizon is, then consequently nobody can observe what is behind it (even via gravitational effects), i.e. what is behind it becomes unobservable and hence not something that can characterize the black hole. But for everybody to agree on what's inside a black hole, the system needs to have settled into a static state, which is not the case here. Hence the no-hair theorem doesn't apply. Is this correct? $\endgroup$ – user541686 Feb 11 '19 at 8:38

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