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:
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- 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.
