But my physics intuition tells me that as two of them merge, the resulting BH should have a "peanut" shape, at least initially.
And maybe it can keep having an irregular shape, depending on the mass distribution inside it?
https://en.wikipedia.org/wiki/Kerr_metric
https://arxiv.org/pdf/0706.0622
https://en.wikipedia.org/wiki/Ergosphere
https://en.wikipedia.org/wiki/Cauchy_horizon
Edit: Updated the bit about about horizons as I research a bit more. It's complicated, and I'm still not positive I have it exactly right, but I think it's now as good as I can get it.
Here's the best resources I've been able to find on the question. Roy Kerr himself responded to the Quora question:
> There is no Newtonian singularity at the Center of the earth and there is no singularity inside a rotating black hole. The ring singularity is imaginary. It only exists in my solution because it contains no actual matter. When a star collapses into a black hole it keeps shrinking until the centrifugal force stabilizes it. The event shell forms between the star and the outside. In 57 years no one has actually proved that a singularity forms inside, and that includes Penrose. instead, he proved that there is a light ray of finite affine length. This follows from the “hairy ball theorem”.
The stack overflow answer seems to describe the problem in terms I can better understand:
> It seems unlikely to me that you're going to be able to formulate a notion of diameter that makes sense here. Putting aside all questions of the metric's misbehavior at the ring singularity, there is the question of what spacelike path you want to integrate along. For the notion of a diameter to make sense, there would have to be some preferred path. Outside the horizon of a Schwarzschild black hole, we have a preferred stationary observer at any given point, and therefore there is a preferred radial direction that is orthogonal to that observer's world-line. But this doesn't work here.
https://physics.stackexchange.com/questions/471419/metric-di...
https://www.quora.com/What-is-the-typical-diameter-roughly-o...
It’s wild how much happens in those milliseconds though. Numerical relativity papers like the one you shared from arxiv.org show the horizon “sloshing” before it stabilizes.
If singularities are real...same thing but more boring answer maybe? (the distribution just being: in the center).
You only get an asymmetric black hole during the milliseconds of a merger. And that asymmetry is entirely due to the mass distribution inside the black hole. The black hole only becomes spherical again once the singularities have merged. Or in the more common case of rotating black holes, they only become properly oblate again once their ringularities have merged. Either way it happens quite quickly.
I think that concept might fit with the infinite time dilation preventing a merger from ever actually occurring? I'd be curious how that might differ for matter that's already inside when the critical mass is reached. (I'd also be curious to know all the creative and wacky ways in which I got the above completely wrong given that's just about inevitable.)
The point where our notions of geometry would break down would be near the singularity, not near the horizon, and we don't even know if a volume enclosed by a horizon (i.e. anything you might call a black hole) necessarily has a singularity inside, it's just that our simple mathematical models all assume one.
It is even the case that once two black holes have overlapping event horizons (so they "touch" in a way) they can't stop touching. So two black holes can zip past one another at a small distance, but if they high-five they can't stop merging.
What does curvature mean? It means that the direction of time’s arrow is different in different places. To an observer outside of a large gravitational field, events inside the field appear to move more slowly than they would have outside of it. Black holes merely take this to an extreme. To an observer far from a black hole, a clock entering the black hole appears to slow down and finally _stop_ as it crosses the event horizon¹. But simultaneously an observer traveling with the clock observes something different. They see everything outside the black hole slow down and stop instead, while they continue to coast smoothly along. They notice nothing strange at the horizon itself; it is simply empty space with weird visuals in the distance.
This almost seems like a paradox, since the two observers each believe that the other’s clock has stopped. The reason why it’s not a paradox is that the space around the black hole is strongly curved, so strongly that the axis of time swaps place with one direction of space. At the horizon the axis of time flips over and points down into the black hole. The distant observer sees time stop because time is now edge–on, as it were. The observer falling into the black hole notices nothing weird near themselves, because both time and space still exist. Only the images of distant objects show any evidence of curvature. But the falling observer is doomed, for their own time axis now points at the singularity. Their timeline now ends abruptly, while the timeline of the distant observer extends potentially a vigintillion years.
For some edutainment on the subject, I recommend The Science Asylum. He’s done a bunch of videos on gravity and relativity, but here are two in particular:
* Explaining Gravity Using Relativistic Time Dilation <https://www.youtube.com/watch?v=F5PfjsPdBzg&list=PLOVL_fPox2K83_36YgnGisn4rxNvgq1iR&index=7>
* Why Can't You Escape a Black Hole? <https://www.youtube.com/watch?v=yPQUtuTraxs&list=PLOVL_fPox2K-zpTeryROTkmzzsMssSMWp&index=6>