A simple Black Hole question I can't find an answer for

[davel18]

I apologize if I'm posting in the wrong part of the forum, I'm new. I have started find cosmology interesting. I have started to learn about black holes but I don't understand something that might obvious and I'm not getting it.

Why is/was there an assumption that things that enter a blackhole are destroyed? I totally get that things that pass the event horizon will never be able to escape but how did we get from never coming out again to destroyed? I get the whole spaghettification thing and while that would seriously warp anything that entered a black hole and hit the singularity, however warping isn't destroying though. It seems like things like Hawking Radiation are based on something we have no evidence for. Displaced, warped stripped down to atoms aren't 'destroyed" which is something we know can't happen in the first place. So how to we get from one point to the next?

Thank you for your time.

 

[Ibix]

In a classical black hole, singularities are the edge of the map we can draw of spacetime. Things that reach there fall off the edge of the map. Presumably that doesn't happen in reality, but we don't know what does happen.

In our models, singularities are usually (always?) surrounded by regions of spacetime where the curvature increases without bound. That means that eventually anything will be torn apart before it reaches the singularity because it would need to be infinitely strong to hold together against the curved spacetime inducing different parts of it to move in different directions. Again, note that we suspect the "edge of the map" is probably a result of our models failing somewhere just short of there, so the curvature rising without bound may be part of the model failing, so something else may happen in reality.

Hawking radiation is completely separate topic. It's related to quantum field theory at the horizon, not near the singularity. As far as I understand it it's related to thermodynamic concerns.

 

[PeroK]

The singularity is where the mathematical model breaks down. It isn't a physical thing. Anything that crosses the event horizon only has a finite time before the singularity, where its time (according to GR) runs out.

I guess at some stage such an object would be considered to have been destroyed.

A theory of quantum gravity is expected to supersede GR and fix the mathematical model, I.e. get rid of the singularity.

 

[PeterDonis]

Why is/was there an assumption that things that enter a blackhole are destroyed?

It's not an assumption; it's a conclusion based on what the mathematical model tells you. The mathematical model tells you that once something falls inside the horizon, it only has a finite amount of time left to exist. That's not something that was put into the model; it's what comes out of it after it's constructed.

As @Ibix and @PeroK have said, we expect that the mathematical model that tells us that is not actually correct--that at some point before the singularity, that model breaks down, and we'll have to replace it by a different model. But we don't have any other model to replace it with at this time.

 

[javisot]

Perhaps the first thing you need to know is why you haven't asked your question in the right place. A black hole isn't cosmology; it's astrophysics. The difference between cosmology and astrophysics, both branches of physics, is that astrophysics studies astrophysical objects (for example, black holes, planets, etc.), while cosmology studies cosmological objects.

 

[PeterDonis]

A black hole isn't cosmology; it's astrophysics.

At PF, we've had questions about black holes in a number of forums.

This particular question, since it's really about the basic mathematical model of a black hole, best fits in the relativity forum, and I have now moved it there.

 

[Dale]

I get the whole spaghettification thing

Umm, that is what destroys things. The tidal forces grow without bound.

Any object composed of multiple fundamental particles will have some finite maximum tidal force that it can withstand before being destroyed. That structural limit will be reached before the singularity.

Yes, we expect the GR model to fail at the singularity, but the tidal forces will exceed any finite threshold before the singularity.

stripped down to atoms aren't 'destroyed"

Well, I certainly would consider myself to be destroyed if I were stripped down to atoms. But even atoms will be pulled apart. It is hard to envision a reasonable definition of “destroyed” under which that wouldn’t qualify.

 

[Matterwave]

In our models, singularities are usually (always?) surrounded by regions of spacetime where the curvature increases without bound.

A few points of clarification here.

"Curvature increases without bound" (assuming you mean some kind of scalar measure of it anyways) is one conception of what happens at a singularity, but it's not the one used in the singularity theorems of Penrose and Hawking. Those theorems only prove that under certain conditions there exists (a) inextendible causal curve(s) which has finite proper time (at least in one direction).

Second, it seems you are talking about the cosmic censorship conjecture with the use of ("always"), please correct me if I'm wrong! In that case, the conjecture states that singularities (except for the big bang one) is hidden behind a horizon. In that case, it requires some strong conditions to hold (and it's still a conjecture). So if by "models" you mean "solutions to EFEs" then "strictly" the cosmic censorship conjecture is false. One can construct fine-tuned counter examples e.g: Violation of cosmic censorship in the gravitational collapse of a dust cloud | Communications in Mathematical Physics | Springer Nature Link https://share.google/eF0fHBCed0A2EwVm4

 

[renormalize]

"Curvature increases without bound" (assuming you mean some kind of scalar measure of it anyways) is one conception of what happens at a singularity, but it's not the one used in the singularity theorems of Penrose and Hawking. Those theorems only prove that under certain conditions there exists (a) inextendible causal curve(s) which has finite proper time (at least in one direction).

No, that statement is too restrictive. It's true that the singularity theorems of GR are defined in terms of geodesic incompleteness, but it's also true that physical quantities diverge at a spacetime singularity. See Recent Developments in Gravitational Collapse and Spacetime Singularities for the following quote:

 

[Matterwave]

No, that statement is too restrictive. It's true that the singularity theorems of GR are defined in terms of geodesic incompleteness, but it's also true that physical quantities diverge at a spacetime singularity. See Recent Developments in Gravitational Collapse and Spacetime Singularities for the following quote:
View attachment 372637

"Typically". Am I missing something?

 

[PeterDonis]

it's not the one used in the singularity theorems of Penrose and Hawking

Which doesn't matter, because for black hole solutions (the Kerr-Newman family of solutions), we don't use the singularity theorems to tell us that curvature increases without bound as the singularity is approached. As you note, that would be useless since the singularity theorems don't show any such thing. We explicitly compute the relevant curvature invariants and show that they increase without bound as $r \to 0$.

 

[Matterwave]

I'm not trying to be restrictive in terms of "physically reasonable scenarios". My statement is only restricting what the singularity theorems prove. If you read through those theorems, they rely heavily on the concept of congruences of geodesics of the spacetime and showing that they must be incomplete.

 

[Matterwave]

Which doesn't matter, because for black hole solutions (the Kerr-Newman family of solutions), we don't use the singularity theorems to tell us that curvature increases without bound as the singularity is approached. As you note, that would be useless since the singularity theorems don't show any such thing. We explicitly compute the relevant curvature invariants and show that they increase without bound as $r \to 0$.

Sure, agree on that.

 

[PeterDonis]

it's also true that physical quantities diverge at a spacetime singularity.

Not necessarily. Note that your reference says "typically", not "always". What "typically" appears to mean is "in black hole solutions where we can explicitly compute the relevant curvature invariants". As I noted in post #11, that's how we actually know that curvature increases without bound as $r \to 0$ in a black hole. The singularity theorems have nothing to do with it.

 

[Matterwave]

Sorry if me bringing in the singularity theorems derailed the conversation. I only meant to clarify what has been proven vs what has not been proven.

 

[PeterDonis]

I only meant to clarify what has been proven vs what has not been proven.

What has/has not been proven by the singularity theorems, yes. But the calculations that show that in specific solutions, such as the Kerr-Newman family of black hole solutions, curvature does increase without bound as the singularity is approached, are also proofs. They're just different proofs from the ones in the singularity theorems.

 

[Matterwave]

What has/has not been proven by the singularity theorems, yes. But the calculations that show that in specific solutions, such as the Kerr-Newman family of black hole solutions, curvature does increase without bound as the singularity is approached, are also proofs. They're just different proofs from the ones in the singularity theorems.

True statement. I did not mean to imply the opposite.

 

[martinbn]

What has/has not been proven by the singularity theorems, yes. But the calculations that show that in specific solutions, such as the Kerr-Newman family of black hole solutions, curvature does increase without bound as the singularity is approached, are also proofs. They're just different proofs from the ones in the singularity theorems.

I may be wrong, but the way I understood him, was that this is a calucation for a very specific family of solutions. The singularity theorems are generic and the nature of the singularities is not clear. It may be expected to be like the calculations, but it is not proven in the general case.

 

[Ibix]

This is a High School level thread. I think the singularity theorems may be a bit above the OP's current level.

In #2 I see I did say "singularities usually...", but I was only thinking of black hole singularities in the context of this thread. I'm not familiar with any true black hole solutions that don't have some scalar curvature measure (I deliberately left out the "scalar measure" bit at this level) that diverges as you approach the singularity. But there may be a type I missed.

 

[pervect]

I apologize if I'm posting in the wrong part of the forum, I'm new. I have started find cosmology interesting. I have started to learn about black holes but I don't understand something that might obvious and I'm not getting it.

Why is/was there an assumption that things that enter a blackhole are destroyed? I totally get that things that pass the event horizon will never be able to escape but how did we get from never coming out again to destroyed? I get the whole spaghettification thing and while that would seriously warp anything that entered a black hole and hit the singularity, however warping isn't destroying though. It seems like things like Hawking Radiation are based on something we have no evidence for. Displaced, warped stripped down to atoms aren't 'destroyed" which is something we know can't happen in the first place. So how to we get from one point to the next?

Thank you for your time.

I'm not sure why you think there is any effect other than spaghetification. I would have said that the reason people say that black holes destroy things is due to spaghetiffication, rather than anything more exotic.

Onto hawking radiation.

We don't have any direct experimental observation of Hawking radiation, though it remains a mathematical prediction from quantum field theory in curved spacetime. There's a related effect that is predicted to occur due simply to large enough accelerations with no black hole needed called the Unruh effect. That doesn't have any experimental evidence either, but it shedds some light

I believe there has been some experiments for phenomenon that are analogous to black holes that have shown that the analogs have phenomenon that would be equivalent to Hawking radiation in an actual black hole. See for instance https://arxiv.org/abs/1409.6550. (This is the abstract, the PDF of the full paper is available on the same site).

There are no black holes in this experiment, but the relevant math is shared by the GR formulation of a black hole, and the actual system studied which involves a Bose-Einstein condensate.

As others have noted, Hawking radiation is separate from the main question - it doesn't occur at the singularity, but at the event horizon. I would say it's the accepted paradigm even lacking direct experimental evidence.

Back to the topic of the interior of black holes.

The problem of what happens inside the event horizon of a real black hole is probably untestable, at least classically. (I'm not familiar enough with the quantum effects to say how they might change things).

Note that the usual BH model that is discussed in forums like PF is the Schwarzschild black hole, which is highly idealized and probably unstable. There is literature on what the interior space-time geometry of an actual black hole is expected to be, but it's difficult for me to evaluate.

If one is willing to step slightly outside GR, there are black hole models that 'bounce' rather than collapse to a singularity. These are based on Einstein-Cartan theory rather than GR. The two theories make essentially the same predictions under any conditions that are currently accessible for testing, they only differ under really extreme conditions.

Einstein-Cartan theory arises fairly naturally, but it's more complex than GR due to the presence of spin effects, so usually people use the simpler theory.

So, to sum up, there's some question as to what a realistic black hole interior would look like in GR, and there' are more questions as to whether GR is correct under the extreme conditions we might expect inside a BH. The scientific method suggest experiment is the way to make such decisions as to which theory to use, but we aren't able to observe the interior regions of black holes and/or sufficiently extreme conditions to make such a decision.

 

[javisot]

Why is/was there an assumption that things that enter a blackhole are destroyed?

I'm not sure if this question refers to "destroyed" by spaghettification, or to the information problem (since it mentions black holes and Hawking radiation, therefore QFT).

 

[PeterDonis]

I'm not familiar with any true black hole solutions that don't have some scalar curvature measure (I deliberately left out the "scalar measure" bit at this level) that diverges as you approach the singularity. But there may be a type I missed.

The Kretschmann invariant increases without bound as $r \to 0$ in the Kerr-Newman family of solutions, which AFAIK is all black hole solutions.

 

[PeterDonis]

this is a calucation for a very specific family of solutions.

The calculation of the curvature invariant increasing without bound is for the specific Kerr-Newman family of solutions, yes.

The singularity theorems are generic and the nature of the singularities is not clear.

More precisely, the singularity theorems only show geodesic incompleteness; they say nothing whatever about the specific behavior of any curvature invariants.

 

[PeterDonis]

There is literature on what the interior space-time geometry of an actual black hole is expected to be, but it's difficult for me to evaluate.

The geometry that appears, at least in numerical simulations, to be stable under small perturbations is the BKL singularity, or "mixmaster" singularity, which is an attempt to describe the chaotic behavior of the curvature as $r \to 0$. This would destroy any kind of object even more effectively than the "spaghettification" of the exact Schwarzschild geometry.

 

[Ibix]

The Kretschmann invariant increases without bound as $r \to 0$ in the Kerr-Newman family of solutions, which AFAIK is all black hole solutions.

All eternal black holes, yes. It's true of Oppenheimer-Snyder black holes too, since they are a patchwork of FLRW "Big Crunch" and Schwarzschild black hole. I think the only other true black hole I know is the Vaidya black hole, which I believe is a modification of the Schwarzschild black hole so I expect has the same singularity, but I haven't checked.

 

[PeterDonis]

the Vaidya black hole

If you mean the ingoing Vaidya metric, yes, that basically works the same as the Oppenheimer-Snyder collapse model, except that what's collapsing is ingoing null radiation instead of matter. IIRC the singularity at $r = 0$ is the same.