> it would be sucking up the matter on the walls as well

It won't. The first time it touches (or comes near) the wall it will take what it can get, but it will never go farther than that. There is nothing that will "push" it closer to the walls.

You are missing the crucial point. The force in a cave in the middle of the earth is ZERO, there is NO force directed to the center of the cave. This is not an intuitively correct statement, but if you carry out the calculation you will see that it is true. If you take a solid sphere and carve out a spherical cave in the center, then everywhere (not just in the center) inside this cave all the little forces from all the atoms of the big solid sphere cancel out.

So this means that inside the cave the black hole will just move in one direction, until it hits the wall. Then it will suck up some mass and be pulled back to the center. Then it will suck up some mass on the other side, etc.

The only way the black hole will remain in the cave is if you put it in the cave with exactly zero velocity to begin with. As soon as one atom falls into it it will start to eat up the earth.

No, I am not missing that point.

You are missing a point.

Yes, inside the cave there is no force. But the black hole can hit the wall just once. After that it can not go any farther.

If passes thought/inside the wall it will be pulled back to the center, and the momentum exchange with the earth will slow it down (so next time it won't go as far). If it was just touching the wall, then that is as far as it can possibly go.

So once it's inside it's little cave, it's done. It can't eat anymore. (Unless of course there is no cave and the earth feeds it, but we are assuming a cave.)

You are missing three points: one is that if there is no cave, and it's oscillating through the earth, it will be pulled to the center. Two is that it looses momentum each time through the earth. And three is that once it's inside it's hollow cave it can no longer reach the wall.

I don't know what to say. On one hand you seem to agree that there is no force to slow the black hole down inside the cave, but on the other hand you claim that the black hole will remain inside the cave.

> You are missing three points: one is that if there is no cave, and it's oscillating through the earth, it will be pulled to the center.

Agreed.

> Two is that it looses momentum each time through the earth.

I'm not so sure about that. Mass is added to the black hole, and perhaps this causes the total momentum to increase.

> And three is that once it's inside it's hollow cave it can no longer reach the wall.

If it is stopped inside the cave. But there is no force to stop it.

Well we agree on the basics, that's good.

Imagine a tiny black hole arriving on earth. It grabs some mass. The black hole is moving, but the mass it ate is not. So rather than free falling, it looses momentum. As it falls through the earth it keeps doing that.

So it will not rebound back up to the top at the same height it fell. It will be lower. The second time through the same thing will happen.

Each time it oscillates it will get lower and lower.

Next. Say the black hole is a bit bigger. And it eats some mass on one side of the earth - now there is an imbalance. There is more mass on the other side. So the forces will cause it to slow down more than it otherwise would.

When it finally settles down enough to make a cave, it will "swing" as much as it can. But each swing can not be any higher than the one before. Over time, with random atoms falling into the cave it, it will come to rest at the exact center.

Assuming the cave is spherical, each swing will reach the other side, because inside the cave the black hole will not be slowed down, do you agree? So in this perfect situation, it is impossible that the black hole will come to stop exactly in the center. Even if it was stopped exactly in the center, if one atom hits it from one side, the black hole will crash into the other side (but slowly of course).

I see your point (I didn't before).

There is no force on the black hole, so if it moved at all it would crash into the wall. Only when it actually ate some of the wall would it turn around. So each swing would eat more and more.