[wallace_f]

>In the former case I’d bet that it turns out the wave would form within the event horizon of the hole, and that’s a good as saying it would never form.

Sorry if this is a bit naive and tangential, but I've always stumbled at the thought of how does gravity-information about the interior of a black hole propagate out of the event horizon? ...Gravitons/gravity waves travel at, c?

[scottie_m]

That’s a bit of a tricky question, because it’s math-heavy. The best way to describe it is to think of the event horizon as the black hole, and forget that there is even an interior. The black hole can be fully described by the conditions at the event horizon after all, and everything else is cut off from the surrounding universe completely. In that sense there is no propagation from the interior at all, which is good because if information could escape then theories describing black holes would be broken.

Instead the black hole has mass, charge, and momentum (three kinds of momentum actually, but that’s not important). Whatever is going on beyond the event horizon, whatever that might be, has no effect that anyone can detect. Matter is accreted “onto” the event horizon which then expands in proportion to the mass of the volume of the hole. Maybe it’s destroyed beyond that point, or maybe it goes to another universe, but we can never know. The event horizon can also shrink if the surroundings are sufficiently cold (really really really cold) and the horizon is sufficiently hot.

Still, all of this is surface phenomena, like dropping a bowling ball into a tub of water. The water only “knows” about the surface of the ball, which which gets properties from the whole ball without exposing the center. A bowling ball in water creates waves, but the interior isn’t interacting with the water anymore than the black hole interior interacts with space (assuming an idealized perfectly rigid bowling ball). In the same way gravity waves or fractions would be a function of how the space just beyond the event horizon is warped.

Does that help?

[thaumasiotes]

I have some naive questions too. This is basically just me rephrasing the question I understood wallace_f to be asking:

- The event horizon is a two-dimensional sphere and, being two-dimensional, has zero mass and cannot exert any gravitational force.

- The black hole within the horizon is a three-dimensional massy object and can and does exert a lot of gravitational force.

- Assume at equilibrium our black hole is somehow exerting gravitational forces on its surroundings which are what you would predict if you accurately knew the black hole's actual mass.

- Assume the black hole moves, e.g. because of inertia.

- Now it should be exerting more force than previously on one half of the universe (the half it moved toward), and less force on the other half.

- Say it moved toward you. After a speed-of-light delay, you should actually perceive more force on yourself towards the black hole. But this can't be because a messenger particle was transmitted from the black hole to you. How can it be?

Assuming this shows that black holes cannot move seems unsatisfactory, given the recession of galaxies from one another, observations believed to show black holes colliding, etc. Where are my mistakes?

Followup: one black hole collides with another black hole of roughly ten times its size. Is it necessarily the case that the center of mass of the new, combined black hole ends up at the point that was the center of mass of the small-hole/big-hole system just as the small hole crossed the big hole's event horizon?

[cperciva]

> - The event horizon is a two-dimensional sphere and, being two-dimensional, has zero mass and cannot exert any gravitational force.

Stop right there. A two dimensional surface can have mass if it has infinite density. And infinite density makes as much sense as any other sort of singularity...

[thaumasiotes]

Where's the singularity that occurs if we assume it's just a region of space with nothing in it? I didn't call the black hole a zero-dimensional point.

[scottie_m]

We don’t know, and may have no way of knowing. There are conjectures that the event horizon is it, that inside the event horizon is a quantum fuzz ball, or strings, or 1D points, or a whole universe. We don’t know, and may well never know. What we do know is that it seems a 2D horizon can encode the information required to describe a 3D volume, and that goes for event horizons, as well certain classes of cosmic horizons in some models. This weirdness is the core of the holographic principle conjecture.

[scottie_m]

Ok, I’ll do my best here. I’m going to pass the first question because there’s already a discussion about it below.

I have some naive questions too. This is basically just me rephrasing the question I understood wallace_f to be asking: ... - The black hole within the horizon is a three-dimensional massy object and can and does exert a lot of gravitational force.

The black hole includes the event horizon, which marks the point at which we stop knowing anything or have theories to predict anything. We really have no idea what’s beyond the event horizon, and almost anything you can imagine has been conjectured as being there, from firewalls to elder gods. We’re talking about a region which can’t be properly described by he theories we have, where the manifold ceases to well behaved. Everything beyond the event horizon is causally disjoint with the rest of the universe, and may as well not exist for anything that isn’t falling past the event horizon.

- Assume at equilibrium our black hole is somehow exerting gravitational forces on its surroundings which are what you would predict if you accurately knew the black hole's actual mass.

Right, mass is one of the “hairs” a black hole has along with charge and momentum.

- Assume the black hole moves, e.g. because of inertia. - Now it should be exerting more force than previously on one half of the universe (the half it moved toward), and less force on the other half.

It sort of does, this is the basis of frame dragging when the hole is spinning. The hole warps spacetime around it, dragging reference frames in the direction of its motion.

- Say it moved toward you. After a speed-of-light delay, you should actually perceive more force on yourself towards the black hole. But this can't be because a messenger particle was transmitted from the black hole to you. How can it be? Assuming this shows that black holes cannot move seems unsatisfactory, given the recession of galaxies from one another, observations believed to show black holes colliding, etc. Where are my mistakes?

The theory of gravity we actually have doesn’t involve bosons, it’s a geometric theory describing a continuous manifold. How that squares with theories containing gravitons is well above my pay grade, sorry. The classical theory says that the warping of spacetime is continuous, and so the hole moves like something being dragged through water, including a wake and bow wave. Since the hole can’t move at c, being massive, there is always an acceptable delay for the light-speed propagation of disturbsnces in spacetime to reach you first.

Followup: one black hole collides with another black hole of roughly ten times its size. Is it necessarily the case that the center of mass of the new, combined black hole ends up at the point that was the center of mass of the small-hole/big-hole system just as the small hole crossed the big hole's event horizon?

They end up merging like two legs of a pair of pants meeting at the crotch, with the new center of mass at the barycenter of the previous orbiting pair. I loved these questions by the way, I can tell you put some real thought into them.

[wallace_f]

Thanks for writing that out, very interesting.

I find this concept of a black hole's surface having the contents inscribed on it to be really difficult for me to imagine; but I can take people's word for it, and it does explain away the paradox.

This reminds me that from some vantage points the universe seems so arbitrary sometimes. This is probably just my human intuition, but personally it just appears to me that nature is not really always elegant, but rather has these work-arounds and different layers to it to keep it working. Not unlike my terrible code.