#### [SOLVED] Why don't merging black holes disprove the no-hair theorem?

By zooby

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?

#### @G. Smith 2019-02-10 23:55:55

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.

#### @zooby 2019-02-11 00:01:18

It's an odd theorem because most black holes aren't stable, their either evaporating or each particles from the background space.

#### @niels nielsen 2019-02-11 00:09:13

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.

#### @G. Smith 2019-02-11 00:09:43

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.

#### @Nathaniel 2019-02-11 07:21:37

@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.)

@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?

#### @G. Smith 2019-02-11 16:42:47

@Mehrdad In my opinion, that is not a good way to think about it. The horizon doesn’t keep the mass, angular momentum, and charge of the black hole from being observable.

@G.Smith: I think I wrote that sentence rather poorly ("what is behind it becomes unobservable and hence not something that can characterize the black hole"). I meant to say what is behind it at a particular point in space becomes unobservable... i.e., you can't discern what's going on at particular points behind it (compared to other points). Though the crux of my explanation wasn't really that sentence (which I'm having a hard trouble formulating; I'm hoping the reader can fill in as needed), but the rest of it -- the intuition that people need to agree on the boundary in the first place.

#### @G. Smith 2019-02-11 16:57:34

@Mehrdad I have not seen a discussion of the no-hair conjecture that focuses on the importance of observers agreeing on where the horizon is, so I don’t think this is the crux of it.

@G.Smith: Hm I see, okay thanks.

#### @G. Smith 2019-02-11 17:58:23

@Mehrdad Also, I’m fairly sure that the location of a horizon can be defined in an observer-independent way even when the horizon is not static. So even when black holes are merging and the horizon is moving, observers agree on where it is.

@G.Smith: that seems... very surprising? I have a hard time imagining how that's possible.