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

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Discussion Overview

The discussion centers around the conceptualization of black holes, particularly contrasting traditional 2-D analogies with 3-D representations. Participants explore the implications of visualizing black holes as floating entities in space and the effects on objects that interact with them. The conversation touches on theoretical aspects of black holes, including their mass, depth, and the nature of objects entering them.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants propose that visualizing a black hole as a floating entity leads to questions about its appearance and the effects on objects around it, such as warping of light and the visibility of objects behind it.
  • Others argue that a black hole would appear as a black disk, with significant warping effects for light grazing its event horizon.
  • A participant questions the depth of a black hole in relation to its radius, suggesting that the mass of a black hole is linear with respect to its radius.
  • Another participant challenges the usefulness of analogies like the "stretched sheet," asserting that they can be misleading and do not accurately represent the nature of black holes.
  • There is a discussion about whether objects entering a black hole disintegrate instantly, with some suggesting that tidal forces may not be strong enough at the event horizon to destroy them immediately.

Areas of Agreement / Disagreement

Participants express differing views on the implications of analogies used to describe black holes and the nature of objects entering them. There is no consensus on the depth versus radius relationship or the immediate effects on objects that fall into a black hole.

Contextual Notes

Limitations include the reliance on analogies that may not accurately convey the complexities of black holes, as well as unresolved questions about the nature of tidal forces at the event horizon.

Cody Richeson
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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?
 
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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.
 
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How deep would it be if it were only the size of a beach ball?
 
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.
 
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.
 
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.
 
So is it correct to say that whatever goes in would simply disintegrate instantly? There's no "well" to speak of?
 
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.
 

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