Does a black hole singularity have size within the black hole's event horizon?

[md65536]

I was thinking about how time and space is consistent no matter how it is observed (related to this post: http://www.sciencefo...rves-spacetime/).

 

As an example, suppose you could shrink the universe down to a very small size. It would continue to function consistently with the relationship between time and space being determined by the value c. You may see the universe as small, but others who may perceive it differently may see it as immense.

 

 

I think this is exactly what would happen if you were to somehow "step outside" the universe. You would perceive it as small (as a black hole, I believe), while others inside it would see no change in space or time.

 

If you shrunk it this way and could peer inside, you would necessarily see that time seems sped up*... as light still travels at c, a lot more can happen with smaller distances. And yet, the universe would be consistent for all observers, including you outside and everyone inside.

 

However, if you were to shrink the universe to a singularity, you would "lose track" of its time... I think its time would become undefined to you. Would it still be possible to have a consistent understanding of the universe?

 

As a leap of logic, one might say that if you perceived the universe as a singularity, then it no longer exists consistently for you. If that is true, then there is no way you can perceive information about it. If the universe is viewed as a black hole singularity, then it is at the event horizon that you are no longer able to make observations of it. So would that coincide with the size of the universe? Inside the event horizon, it is observable and thus has size and thus time and is consistent, and outside the horizon it is sizeless and thus unobservable and inconsistent.

 

This might also relate to the idea that what is unobservable does not exist. The reality that may be defined within a singularity is not defined outside of it.

 

 

 

 

Apologies if this is just a mess of meaningless thoughts. Does anyone follow my reasoning, or have related thoughts? Or am I skipping so far over the details (both in my mind and in this post) that all that's left is nonsense?

 

 

* Edit: I may have that backwards? This gets me every time.

Edited February 24, 2011 by md65536

[Spyman]

An observer crossing a black hole event horizon can calculate the moment they've crossed it, but will not actually see or feel anything special happen at that moment. In terms of visual appearance, observers who fall into the hole perceive the black region constituting the horizon as lying at some apparent distance below them, and never experience crossing this visual horizon.

http://en.wikipedia.org/wiki/Event_horizon#Interacting_with_an_event_horizon

[md65536]

An observer crossing a black hole event horizon can calculate the moment they've crossed it, but will not actually see or feel anything special happen at that moment. In terms of visual appearance, observers who fall into the hole perceive the black region constituting the horizon as lying at some apparent distance below them, and never experience crossing this visual horizon.

http://en.wikipedia....n_event_horizon

And moving in the opposite direction is impossible... "In 1958, David Finkelstein identified the Schwarzschild surface as an event horizon, 'a perfect unidirectional membrane: causal influences can cross it in only one direction'."[1] So in my analogy it's impossible to escape the universe completely, as I described it. In fact in my analogy I assume some kind of equivalence between the outside and inside of an event horizon (as a boundary between 2 universes, one might say), which then must be incorrect if it's one-directional.

 

So then it's impossible to compare what would be seen outside, vs inside the EH?

Still, can we say anything about an observer who was always inside the EH? Outside, we calculate there is a singularity at r=0. Inside, might this not be a singularity?

 

I googled it up, and found that what I'm describing is a "coordinate singularity"... a singularity that can disappear with a change of coordinates.

 

It appears that the answer is "no":

"What happens at r = 0? In the Schwarzschild metric, the expressions 2M/r approach infinity as r approaches 0. This is a real, physical singularity, not a coordinate singularity."[2]

 

 

However I'm not fully convinced, because most of the stuff I came across says something like "No one knows what would be seen inside the event horizon" etc, so it could still be a coordinate singularity within the EH.

Also, the singularity is a point singularity only for non-rotating BHs (otherwise it's a ring singularity), and it's likely that all BHs rotate.

Also, the singularities are expected to not be real phenomena, but rather "The appearance of singularities in general relativity is commonly perceived as signaling the breakdown of the theory. ... It is generally expected that a theory of quantum gravity will feature black holes without singularities."[3]

 

 

I can still think of 2 alternatives that would let my idea be true (one where the singularity is a coordinate singularity that disappears inside the EH and one where the singularity remains), but I find no evidence to suggest they have any basis in reality.

 

 

Refs:

1. http://en.wikipedia....hole#Golden_age

2. http://members.cox.n.../black_hole.htm

3. http://en.wikipedia....ole#Singularity

[lemur]

An observer crossing a black hole event horizon can calculate the moment they've crossed it, but will not actually see or feel anything special happen at that moment. In terms of visual appearance, observers who fall into the hole perceive the black region constituting the horizon as lying at some apparent distance below them, and never experience crossing this visual horizon.

http://en.wikipedia....n_event_horizon

It seems like the moment gravitation renders electrons unable to emit photons, something special would happen with matter/energy.

 

edit: I suppose if there is still distance between the emitting particles within the event horizon and their final destination, gravity would/could still pull emitted photons toward the center. But wouldn't both matter and light be falling at the same rate at that point, or would matter continue to fall at sub-C speed while light emitted from it would move at C toward the center?

Edited February 24, 2011 by lemur