Inside a black hole, looking out

[I knows]

I have been pondering black holes for some time and have had trouble with the problems presented simply because there is very little we can do to study the phenomena. I have always thought of a black from the outside looking in, or basically the only way we can hope to see a black hole. However, a thought the other day occurred to me that we may be thinking about black holes all wrong. Why think of a black from the outer perspective when it is the singularity that creates the black hole in the first place. This is purely hypothetical as we all know the singularity is impossible to isolate as it is infinitely small even on the quantum scale. For the purpose of this thought experiment, scale the singularity to our size because the size is really arbitrary. What would the universe look like from our perspective sitting on the singularity looking out? I know the answer, I want to see what others think first...

 

[jedishrfu]

Welcome to PF!

Here's a video simulation of falling into one

 

[Drakkith]

Why think of a black from the outer perspective when it is the singularity that creates the black hole in the first place.

This is incorrect. A singularity does not create a black hole, nor is one required for an event horizon to form. The only requirement is that enough mass be packed into a small enough area. For example, a 1 solar mass object crammed into a sphere the radius of something like 10 km will form an event horizon and a black hole. Whether a singularity will form or not is unknown, as we can't see inside a black hole.

For the purpose of this thought experiment, scale the singularity to our size because the size is really arbitrary.

The size is not arbitrary. Singularities can't be scaled to our size, as they are 0 dimensional objects with no length, width, or depth. You can't scale zero to a non-zero number.

What would the universe look like from our perspective sitting on the singularity looking out?

If we can replace "sitting on the singularity" with "falling into a black hole" we can actually get valid answers, as jedishrfu's video shows.

 

[PeterDonis]

What would the universe look like from our perspective sitting on the singularity looking out?

You can't "sit on the singularity and look out", because the singularity is not a place in space; it's a moment of time. And it's a moment that is in the future for anyone falling into the black hole; so there's no way to "look out" at anything when you reach that moment, since when you reach it you are destroyed.

 

[PeterDonis]

Singularities can't be scaled to our size, as they are 0 dimensional objects with no length, width, or depth.

Technically, the singularity is actually a 1-dimensional object, for reasons which are probably too long to fit in the margin of this thread. But it's still true that you can't "scale" the singularity, because along the one dimension that it does have, it's infinitely long, and you can't scale infinity any more than you can scale zero.

 

[Drakkith]

Technically, the singularity is actually a 1-dimensional object, for reasons which are probably too long to fit in the margin of this thread. But it's still true that you can't "scale" the singularity, because along the one dimension that it does have, it's infinitely long, and you can't scale infinity any more than you can scale zero.

Interesting. I'd never heard this before.

 

[PeterDonis]

I'd never heard this before.

A simple way to see it is to look at Kruskal coordinates. The (future, i.e., black hole) singularity is the (upper branch of the) hyperbola $T^2 - X^2 = 1$ in these coordinates. Every point in the Kruskal diagram represents a 2-sphere with a particular value of the radial function $r$ (which is not a coordinate in this chart, it's a function of $T$ and $X$); on the singularity, we have $r = 0$, so the "2-sphere" at each point on the singularity is actually a zero-dimensional point, and the whole singularity is the curve made up by all of the points where $r = 0$ (which, since it's a hyperbola, has two branches, the upper branch being the future singularity and the lower branch being the past singularity--the latter is not believed to be physically reasonable, but it's there in the full mathematical solution).

 

[.Scott]

Technically, the singularity is actually a 1-dimensional object, for reasons which are probably too long to fit in the margin of this thread. But it's still true that you can't "scale" the singularity, because along the one dimension that it does have, it's infinitely long, and you can't scale infinity any more than you can scale zero.

Does this mean they can hold information?

 

[PeterDonis]

Does this mean they can hold information?

No. Storing information would require that there could be multiple possible states of the singularity, and there aren't. (Technically, the singularity isn't even part of spacetime at all; it's only definable as a limit. But it's still only a single limit, so there's no scope for "holding information".)

 

[marcus]

... Whether a singularity will form or not is unknown, as we can't see inside a black hole...

Drakkith, I tend to agree in a general way. Isn't it controversial what happens at the focus of gravitational collapse? One legitimate view, I believe, is that a singularity is a failure of an older possibly classical theory (not something that exists physically in nature) and that the occurrence of a singularity in a classical model is a mathematical SYMPTOM that the model stops being applicable there and needs improvement, perhaps quantum corrections.
So simply because the older theory develops a singularity need not force one to think that NATURE develops a singularity.

Does this mean they can hold information?

.Scott, as I recall you started an interesting thread about Hawking radiation and entanglement, that touched on various issues, like firewall, and information paradox. Are you at all skeptical about firewall (as a way of preserving unitarity and avoiding duplication of information)? I gather there is no solid consensus in favor of that picture or any other scheme for resolving the various apparent contradictions. Here's that earlier thread:
https://www.physicsforums.com/threads/hawking-radiation-and-entanglement.785913/

Can you think of any alternative to the formation of a "singularity" and would you ask the same question about that alternative? Can that whatever-it-is hold information?

 

[.Scott]

.Scott, as I recall you started an interesting thread about Hawking radiation and entanglement, that touched on various issues, like firewall, and information paradox. Are you at all skeptical about firewall (as a way of preserving unitarity and avoiding duplication of information)? I gather there is no solid consensus in favor of that picture or any other scheme for resolving the various apparent contradictions. Here's that earlier thread:
https://www.physicsforums.com/threads/hawking-radiation-and-entanglement.785913/

Can you think of any alternative to the formation of a "singularity" and would you ask the same question about that alternative? Can that whatever-it-is hold information?

When I asked the question, my thought was that since PeterDonis understood enough about the singularity to know it was 1-dimensional, perhaps he could describe it in terms of information as well.
From what I've read about the firewall, it doesn't exists - at least not as described. First of all, it is not needed. There is no one frame of reference - inertial or otherwise - where there is a problem with unitarity. The issue comes when assuming that a particle has crossed through the event horizon - something that, in principle, does not happen from any frame of reference external to the event horizon. The fact that it does cross through in another frame of reference simply means that the information describing that particle is expressed differently in that frame. Second of all, the event horizon is entirely the product of your reference frame. It will move or disappear depending on where you are and how fast you're traveling and accelerating. So, if I dive into a black hole, when do I hit the firewall? As I cross the event horizon that you see?

Let me put it another way. If you want to say that from the external frame of reference an object is incinerated by a firewall as it crosses the event horizon, fine. But from the external frame, it never crosses the event horizon - so what would that statement mean? If you want to say that the from the objects frame it is incinerated by a firewall, what is the point? From it's frame of reference there is no issue with unitarity.

Also: The firewall wouldn't eliminate information, just transform it. So you still have information dropping towards the singularity.

 

[I knows]

This is incorrect. A singularity does not create a black hole, nor is one required for an event horizon to form. The only requirement is that enough mass be packed into a small enough area. For example, a 1 solar mass object crammed into a sphere the radius of something like 10 km will form an event horizon and a black hole. Whether a singularity will form or not is unknown, as we can't see inside a black hole.
The size is not arbitrary. Singularities can't be scaled to our size, as they are 0 dimensional objects with no length, width, or depth. You can't scale zero to a non-zero number.
If we can replace "sitting on the singularity" with "falling into a black hole" we can actually get valid answers, as jedishrfu's video shows.

This is my first rodeo in this board and realize I need to be more precise in my verbiage.

 

[marcus]

When I asked the question, my thought was that since PeterDonis understood enough about the singularity to know it was 1-dimensional, perhaps he could describe it in terms of information as well.
From what I've read about the firewall, it doesn't exists - at least not as described. First of all, it is not needed. There is no one frame of reference - inertial or otherwise - where there is a problem with unitarity. The issue comes when assuming that a particle has crossed through the event horizon - something that, in principle, does not happen from any frame of reference external to the event horizon. The fact that it does cross through in another frame of reference simply means that the information describing that particle is expressed differently in that frame. Second of all, the event horizon is entirely the product of your reference frame. It will move or disappear depending on where you are and how fast you're traveling and accelerating. So, if I dive into a black hole, when do I hit the firewall? As I cross the event horizon that you see?

Let me put it another way. If you want to say that from the external frame of reference an object is incinerated by a firewall as it crosses the event horizon, fine. But from the external frame, it never crosses the event horizon - so what would that statement mean? If you want to say that the from the objects frame it is incinerated by a firewall, what is the point? From it's frame of reference there is no issue with unitarity.

Also: The firewall wouldn't eliminate information, just transform it. So you still have information dropping towards the singularity.

Nice! Glad to meet another firewall skeptic. :)
I'm also skeptical of the BH singularity idea, think it could be just a mathematical glitch in the model that indicates the model needs improvement (so not to take too seriously).

 

[PeterDonis]

There is no one frame of reference - inertial or otherwise - where there is a problem with unitarity.

Unitarity isn't a property associated with a frame of reference; it's an invariant. Either a quantum process is unitary or it isn't. A quantum process involving a singularity isn't.

The issue comes when assuming that a particle has crossed through the event horizon - something that, in principle, does not happen from any frame of reference external to the event horizon.

Whether or not something happens--like a particle crossing the event horizon--is not frame-dependent; it's an invariant. A particular frame may not be able to describe a particular event happening--for example, the Schwarzschild coordinate chart that covers the region outside the event horizon cannot describe events on or inside the horizon--but that does not mean that whether or not that event happens is frame-dependent. It just means some frames only cover a limited portion of spacetime.

the event horizon is entirely the product of your reference frame. It will move or disappear depending on where you are and how fast you're traveling and accelerating.

This is not correct. The event horizon is an invariant geometric feature of a black hole spacetime. You are confusing the event horizon with a Rindler horizon, which is observer-dependent.

 

[PeterDonis]

it could be just a mathematical glitch in the model that indicates the model needs improvement (so not to take too seriously).

I think this is probably the mainstream opinion of physicists. The question is what improved model (presumably some kind of quantum gravity model, but that still leaves a number of open questions) will supersede classical GR in this regime.

 

[.Scott]

Unitarity isn't a property associated with a frame of reference; it's an invariant. Either a quantum process is unitary or it isn't. A quantum process involving a singularity isn't.

That's right. And every reference frame agrees that there is no violation of unitarity.

Whether or not something happens--like a particle crossing the event horizon--is not frame-dependent; it's an invariant. A particular frame may not be able to describe a particular event happening--for example, the Schwarzschild coordinate chart that covers the region outside the event horizon cannot describe events on or inside the horizon--but that does not mean that whether or not that event happens is frame-dependent. It just means some frames only cover a limited portion of spacetime.

If Alice falls through the event horizon at 12 noon. Nothing that happens to Alice from 12 noon on is part of Bob's universe. You can call it invariant, but it's immaterial to Bob. If you think it does happen in Bob's universe, then the question becomes when? If something happens to Alice at 12:00:01, what time does it happen for Bob? Perhaps 11:50am? If it happens before Alice reaches the horizon, is there still a problem with unitarity?

This is not correct. The event horizon is an invariant geometric feature of a black hole spacetime. You are confusing the event horizon with a Rindler horizon, which is observer-dependent.

If you want to call the event horizon that is seen by external observers as "the event horizon", then it certainly describes an invariant sphere in space. Everyone can calculate where that horizon is as seen from their reference frame, but not everyone will see it as having the extreme transformations commonly associated with an event horizon. So, although a particle can determine when it crosses "the event horizon", it will not experience it as an event horizon.

 

[PeterDonis]

every reference frame agrees that there is no violation of unitarity.

This is not correct if a singularity is present; then anyone using a reference frame that includes worldlines reaching the singularity will see violations of unitarity. The only reason other frames will not see such violations is that they can't cover the region of spacetime that includes worldlines reaching the singularity. But the standard of whether something "happens" is not whether it is included in a particular reference frame, but whether it is included in spacetime. Worldlines reaching the singularity are included in spacetime.

If Alice falls through the event horizon at 12 noon. Nothing that happens to Alice from 12 noon on is part of Bob's universe.

If by "Bob's universe" you mean "spacetime", this statement is incorrect. The correct statement is that nothing that happens to Alice from 12 noon on (according to Alice's clock) is covered by the reference frame you are assuming Bob to be using (but there is nothing that requires Bob to use this frame; he could perfectly well use another one that does cover Alice's worldline from 12 noon on). Another correct statement would be that no light signal emitted by Alice from 12 noon on by her clock will ever reach Bob; but there is nothing that requires Bob to use a reference frame that only includes events that can send light signals to him.

If by "Bob's universe" you mean, not all of spacetime, but just a portion of it, then of course you can make your statement trivially true by picking the portion appropriately. But that isn't physics, it's playing with words.

If you think it does happen in Bob's universe, then the question becomes when?

"When" is not a physical thing; it's a convention. There are conventions that assign a well-defined "when" to events on Alice's worldline from 12 noon on, and there are other conventions that do not. None of that affects any physical things.

If you want to call the event horizon that is seen by external observers as "the event horizon", then it certainly describes an invariant sphere in space. Everyone can calculate where that horizon is as seen from their reference frame, but not everyone will see it as having the extreme transformations commonly associated with an event horizon. So, although a particle can determine when it crosses "the event horizon", it will not experience it as an event horizon.

The event horizon is a globally defined surface: it's the boundary of the region of spacetime (the "black hole") that cannot send light signals to future null infinity. It doesn't depend on any observer or any reference frame; there's no such thing as "the event horizon as seen by external observers", as distinct from some other observers' notion of a horizon. There's just the event horizon, period.

As for "extreme transformations", I don't understand what you mean; but the properties of the event horizon are invariant and don't depend on any observer or any reference frame.

As for what it means to "experience it as an event horizon", if you just mean that an observer falling through the event horizon does not observe any unusual phenomena locally, that's true. But I don't understand what it has to do with the rest of your statements.