Holes in a 2-D surface and holes in 3-D space

[Cody Richeson]

I was watching a panel discussion on YouTube in which Neil DeGrasse Tyson made a very interesting remark about black holes. He said that we traditionally think of holes as indentations in a 2-D surface, such as a hole dug into the ground, and that it didn't make sense to imagine a hole floating in the room he was in, attached to nothing. But why don't we imagine just that: A hole, about the size of a beach ball, floating in the middle of a room. Would you just see a fuzzy black disk that appears the same from all angles, or would it be a fuzzy black sphere? Would you see bizarre geometric warping around its event horizon? If it was sufficiently small and you inserted say, a long stick into it, would you simply see nothing where the stick would be expected to poke through?

 

[Muphrid]

There would be some warping involved, so that if your line of sight would graze the edge of the horizon, you would see something that's actually behind the hole (stretched out and distorted, but still behind).

The hole itself would be black.

If in inserted a rod into it, not only would the rod not come back out the other side, but as soon as you started to retract it, you'd find that the rod had been eaten away or chopped off as far as you stuck it in.

Edit: the thing is, even a hole that is only 1 meter in radius would have a mass of over 100 Earths.

 

[Cody Richeson]

How deep would it be if it were only the size of a beach ball?

 

[Muphrid]

Deep? I don't know what you mean. Massive, maybe?

Mass of a black hole is linear with respect to radius (or vice versa). So even a hole half or a third of a meter in radius would be many, many times more massive than planet Earth.

 

[Cody Richeson]

I know the bowling ball analogy isn't completely reliable, but the well that is formed by a black hole using that type of visualization is very "deep," that is, the vertical length of the well (when thinking of space as a flat, flexible sheet) is much longer than the radius of the black hole itself. So what I'm basically asking is whether or not the depth of the black hole is greater than its radius.

 

[Bill_K]

This is a perfect example of why such analogies are actually harmful and should not be used. The only purpose of the "stretched sheet" is to convey in a simple way the idea that the central mass causes the spacetime around it to become curved. The vertical direction or "depth" has no meaning, and in no way corresponds to reality.

 

[Cody Richeson]

So is it correct to say that whatever goes in would simply disintegrate instantly? There's no "well" to speak of?

 

[Muphrid]

Instantly? No, not necessarily. Only tidal forces will start destroying any object that falls inside, and they need not be strong enough at the event horizon to destroy anything. There's just no way for any object, once inside, to emerge from the hole.