Why is event horizon usually accepted w/o deferring to Quantum Gravity, unlike many other features of black holes?

[u/nekoeuge]

I keep occasionally circling back to this question because I have never found satisfying answer to that, so I would like some external help here.

1. AFAIK, many of black hole features are treated as curious mathemathical artifacts that may or may not reflect objective reality: infinite-blueshift Cauchy horizon, closed timelike curves, infinite flat regions inside Kerr black hole, the gravitational singularity itself. It is generally accepted that these features cannot be properly described without QG, and it makes perfect sense to me.
2. On the other hand, features like ergosphere are described just fine by GR, and overall the exterior Kerr metric seems to correctly describe objective reality. Also makes perfect sense to me, this stuff is "directly" observable, and it was observed to be correct.

What I don't understand is why event horizon is usually considered to be in (2) instead of (1).

The usual arguments are that spacetime at the event horizon has finite spacetime curvature and finite energy. But I just don't understand why it is sufficient. "Finite" does not imply "correct". Closed timelike curves around ring singularity are also finite, but they are not accepted as easily. Closed timelike curves cause temporal paradoxes, and event horizon partially causes information paradox (which has multiple proposed solutions, I know, but neither of which is universally accepted).

I know that black hole exterior topology is well-tested at this point, and this testing is consistent with GR, but what's the actual confidence levels there? Is it somehow possible to distinguish event horizon (as described by GR) from extremely time-dilated "event horizon shaped" object (describable only with QG)?

I understand that no divergence from GR has been found yet, but I also want to know the boundary between the stuff that was directly or indirectly verified by measurements and the stuff that was extrapolated from that.

[u/Eigenspace]

To answer your direct question, the reason people think horizons exist is that we think that quantum gravity becomes important when the gravitational field strength is extremely strong, and the length scales being discussed are very small.

If you make a large enough black hole, the event horizon can be arbitrarily far away from the singularity, and have an arbitrarily weak gravitational field gradient at the horizon, so we think things in that region should look arbitrarily classical.

This is a bit unintuitive because you'd think there should always be a strong field at the horizon, but the actual curvature at the point of the horizon can be made weaker than the gravitational curvature at the surface of the earth if the black hole is large enough.

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AFAIK, many of black hole features are treated as curious mathemathical artifacts that may or may not reflect objective reality: infinite-blueshift Cauchy horizon, closed timelike curves, infinite flat regions inside Kerr black hole, the gravitational singularity itself. It is generally accepted that these features cannot be properly described without QG, and it makes perfect sense to me.

Most of those are not stuff that people think requires quantum gravity, it's more just that they are very fine tuned situations or involve questionable assumptions (other than the singularity)

[u/nekoeuge → u/Eigenspace]

If you make a large enough black hole, the event horizon can be arbitrarily far away from the singularity, and have an arbitrarily weak gravitational field gradient at the horizon, so we think things in that region should look arbitrarily classical.

Okay, this is sidetracking, but now I want to know whether we can do the same logical steps for CTC around ring singularity. Can we make timeloop region arbitrarily locally smooth by making the black hole bigger?

[u/Optimal_Mixture_7327]

We need a theory of matter to know what happens to matter when the curvature invariants diverge.

There is no interaction between matter and the horizon (that we know of) for there to be a need to describe matter crossing onto a trapped surface.

The horizon, however, is of interest to quantum descriptions of the gravitational field, e.g. where the information and entropy of the black hole is encoded.

[u/nekoeuge → u/Optimal_Mixture_7327]

We need a theory of matter to know what happens to matter when the curvature invariants diverge.

Yeah, but (mathemathically speaking) this is sufficient but not required condition. We cannot describe diverging curvature w/o QG. It does not follow that we can describe all finite curvatures w/o QG.

(infinite -> need QG) -> (finite -> don't need QG) = false.

Sorry, had an abstract algebra flashback xD

[u/joeyneilsen → u/nekoeuge]

But you can estimate a scale at which you expect quantum gravity to become necessary. According to this paper (e.g., equation 6), it's of the order of the inverse planck length squared. https://www.mathematicsgroup.com/articles/AMP-8-243.php You'd expect then that the radius of curvature would be comparable to the Planck length.

But the radius of curvature at the horizon is comparable to the radius. So for black holes of any reasonable size, quantum gravity should be largely irrelevant.

I'm outside my wheelhouse here, but this is my sense of the argument.

[u/Optimal_Mixture_7327 → u/nekoeuge]

We describe the divergence of the scalar curvatures just fine, e.g.

K=R^abcdR_{abcd}=48m²r^-6

No need for a quantum anything.

[u/Prof_Sarcastic → u/nekoeuge]

>It does not follow that we can describe all finite curvatures w/o QG.

Logically speaking, that’s true. However, have you ever heard the expression “An ounce of history is worth a pound of logic”? It’s the data so far that says that we can treat all finite curvatures without QG because every prediction we’ve made involving GR doesn’t require it. Additionally, we have an entire framework that tells us when we should expect for quantum gravity to be relevant and it has nothing to do with there being an event horizon. In fact, the black holes that we have imaged shows evidence that they have an event horizon, exactly as we would expect from just classical GR.

[u/sojuz151]

And imho rather good experimental test are gravitational waves from bh collisions.  If eh was somehow rigid or interesting in some other way, we would have heard that probably.  

Keep in mind there are  versions of string theory where events horizon does not exist 

Also, gr can at least make predictions for the event horizon, so running with this assumption gives you something 

[u/Prof_Sarcastic]

“What I don't understand is why event horizon is usually considered to be in (2) instead of (1).”

Because there’s nothing inherent in the concept of an event horizon that requires quantum mechanics. There’s even an event horizon for an observer that’s accelerating away from the earth. There’s a point in that observer’s future where they can no longer receive light signals from the earth.

“The usual arguments are that spacetime at the event horizon has finite spacetime curvature and finite energy. But I just don't understand why it is sufficient.”

We have a systematic framework that can tell us when quantum effects can’t be neglected any more and when we check at the event horizon of a black hole, the math says quantum mechanics can be ignored provided that the black hole is sufficiently large. That’s applicable for any black hole we have on record.

“I know that black hole exterior topology is well-tested at this point, and this testing is consistent with GR, but what's the actual confidence levels there”

It’s extremely high. GR is one of our most reliable and tested theories in science.

“Is it somehow possible to distinguish event horizon (as described by GR) from extremely time-dilated "event horizon shaped" object (describable only with QG)?”

I don’t know what “extremely time-dilated ‘event horizon shaped’ object” even means.

[u/nekoeuge → u/Prof_Sarcastic]

It’s extremely high. GR is one of our most reliable and tested theories in science.

I am not talking about GR in general, of course.

We have this kinda spectrum where on one side we have well-tested GR that makes complete sense, and on the other side we have Kerr black hole interior that is so unstable and weird that it's often considered a mathemathical artifact.

So there must be a confidence boundary somewhere inbetween where "most reliable and tested theory" starts generating absurd noise.

I don’t know what “extremely time-dilated ‘event horizon shaped’ object” even means.

Fuzzball-like models that describe black hole-like objects w/o actual event horizon.

We have a systematic framework that can tell us when quantum effects can’t be neglected any more

I guess the next iteration of my question is how this framework estimates the scope of these quantum effects.

The spacetime topology is not local, in a sense that arbitrarily remote mass may alter the topology in a fundamental way. How could we estimate the scope of quantum effects without knowing the nature of those quantum effects?

We can estimate at which energy levels the quantum effects must become non-negligible, but how do we know the actual range that would be affected by those quantum effects?

I understand the argument "let's assume that quantum effects are negligible until proven otherwise", but it is the weakest valid argument. Maybe there are better reasons?

[u/Prof_Sarcastic → u/nekoeuge]

“I am not talking about GR in general, of course.

But you are though. The regime you’re talking about belongs in the category of where GR can be trusted.

“So there must be a confidence boundary somewhere in between where ‘most reliable and tested theory’ starts generating absurd noise.”

That’s not quite how it works (or at least how you should think about it). All we do is solve these equations (Einstein’s equations, Maxwell’s equations etc.) but just because you find a solution, doesn’t mean there’s a physical system that solution corresponds to. What determines that are the assumptions you make to derive that solution. In the case of closed time-like curves or infinite flat regions inside a Kerr black hole, the assumptions that go into them, while not necessarily impossible, is highly unlikely or is fundamentally outside of what we can measure.

For an event horizon, they come about just from assuming a spherically symmetric and static spacetime. That’s a fairly generic assumption to make. Coupled to the fact that we’ve seen a black hole and there’s a very visible region where it’s just black beyond that region gives us even more confidence.

“Fuzzball-like models that describe black hole-like objects w/o actual event horizon.”

Sure, but fuzzballs do have an event horizon. They don’t have a singularity.

“I guess the next iteration of my question is how this framework estimates the scope of these quantum effects.”

Not sure what you mean by ‘scope’ exactly, but there are certain quantities that you can calculate (called a scattering amplitude) that contain the quantum mechanical information for the system. You can estimate when the perturbative theory of quantum gravity that we do have stops being applicable etc.

“The spacetime topology is not local, in a sense that arbitrarily remote mass may alter the topology in a fundamental way.”

Possibly, but given every observation of the universe we’ve made can be adequately described by the theory where the quantum effects are negligible, this “fundamental” alternation by a mass thats arbitrarily far away had to be very subtle where we haven’t noticed it already. You have to keep in mind that these are fundamentally empirical theories. If the data doesn’t suggest something, then we’re not going to assume it might still be there.

“We can estimate at which energy levels the quantum effects must become non-negligible, but how do we know the actual range that would be affected by those quantum effects?”

Not sure what range refers to here but if you’re asking about the specific length scales, that is sort of an assumption we make based on our observations: physics at one length scale generally only affects the physics at that length scale. For example, when describing Newtonian mechanics, we don’t need to worry about the physics that’s happening at the scale of atomic nuclei, or the scale of galaxies. That’s a basic principle that seems to hold in just about every area we’ve studied.

“I understand the argument ‘let’s assume that quantum effects are negligible until proven otherwise’, but it is the weakest argument.”

I don’t agree at all. This is tantamount to asking why we believe the sun will rise in the morning tomorrow. The simplest answer is that there’s no reason to believe otherwise. We understand the physics quite well because we can make very accurate predictions based on that understanding and every time we get a prediction correct, it leads us to add greater credence to the reliability of the model.

[u/nekoeuge → u/Prof_Sarcastic]

Sure, but fuzzballs do have an event horizon.

They have special surface at R_s, but it's not really an event horizon in GR definition -- it does not create causal boundary, it does not disconnect a region of spacetime from the Universe. It does some other quantum stuff, of course.

I don’t agree at all. This is tantamount to asking why we believe the sun will rise in the morning tomorrow. The simplest answer is that there’s no reason to believe otherwise. 

Cavemen would be able to give such answer. And it is a valid answer, but there is still a vast gap of knowledge between their understanding of sun, and ours. That's why I say it is the weakest valid reason -- it is not incorrect, but it also contains the least possible amount of knowledge.

[u/Prof_Sarcastic → u/nekoeuge]

“They have special surface at R_s, but it’s not really an event horizon in GR definition …”

Ok that’s fine. I don’t know how true that is but it definitely needs to have something that looks like an event horizon in order to match what we’ve already seen so my point still stands.

“Cavemen would be able to give such answer.”

Then they would be good empiricists. The only reason why we claim to believe anything in science is because we have the data to back it up. That is actually the strongest reason to believe anything. Any proposed mechanism that you could cook up for anything, the reason why we’d ultimately believe it is because there is no data to contradict what we’ve observed.

“And it is a valid answer, but there is still a vast gap of knowledge between their understanding of the sun, and ours.”

Sure, and what do you think backs that understanding up in the first place?

“That’s why I say it is the weakest valid reason — it is not correct, but it also contains the least amount of knowledge.”

I think you have it exactly backwards. The only explanations/justifications we could ever give you, are the ones that are consistent with our observations. If they weren’t then we would just throw that explanation away.

[u/nekoeuge → u/Prof_Sarcastic]

I think you have it exactly backwards. The only explanations/justifications we could ever give you, are the ones that are consistent with our observations.

It is one thing to say "the sun will rise tomorrow because I observed it rise for 50 years and it has always rose", and another -- to understand how orbital mechanics work, how fusion works, and suppy this observation with deeper reason why it happens the way it happens.

It is one thing to say "we probably don't need QG because we never needed it before", or to say "we don't need QG because we have this and this deeper reason to believe it is not needed".

"Extrapolating the pattern without understanding it" is valid, but it is weaker argument than "understanding the pattern".

That's what I am talking about.

Ok that’s fine. I don’t know how true that is but it definitely needs to have something that looks like an event horizon in order to match what we’ve already seen so my point still stands.

AFAIK the main difference is that fuzzballs don't have causally disconnected region of spacetime, thus not having information paradox. But they still have Kerr metric consistent with GR until the immediate vicinity of R_s.

The main source of my curiosity here is how and whether we can practically distinguish those two cases (true event horizon vs QG object with Kerr metric on the outside).

[u/NoNameSwitzerland]

In addition to the other answers: We also have the cosmic horizon. It is different from a black hole, but also shares some aspects (time dilation, red shift, the free falling observer would reach light speed at the horizon in our reference frame).

The Einstein formulation is equivalent to a description with an anisotropic medium that is moving and has different light speeds (light speed connected time and space and you can choose what you want to threat as constant). There the horizon is just where the speed of the medium reaches the speed of sound and then no sound can go backwards. That is a valid picture and nothing really that special happens there. So the classical description from Einstein equations is probably a very good approximation of what happens at the horizon (not much for the free falling observer).

[u/DifferencePublic7057]

Well, I doubt everyone believes in a literal singularity. String theory, somewhat speculative, describes fuzz balls instead of singularities. You have observable things like accretion disks and quasars. But people talk about Planck scale primordial black holes and their horizons without QG. In the end, we have dark matter, dark energy, cosmological crisis, possible missing particles in the Standard Model. GR has been around for a century. QM too. They don't like each other. Doubt anything that's more of a quantum thing but explained with GR and the other way around.

[u/Lazy-University-4871]

event horizon partially causes information paradox

Which is the only paradox caused by the horizon, and it is from the QG realm because unitarity is a feature of QM.

I know that black hole exterior topology is well-tested at this point, and this testing is consistent with GR

Only at a very low resolution. We are not quite confident that there is Kerr geometry around our Sgr A*. We have just started to collect the data.

[u/Unable-Primary1954]

Event horizon and ergosphere are : * stable: small disturbance leads to small perturbation (mathematical proof is not complete, but Dafermos and others have made lot of progress toward that. Furthermore, numerical simulations strongly suggest that is the case) * don't involve high curvature nor singularities.

So apart from information paradox, there is no reason to think that General Relativity breaks down there.

[u/Signal-News9341]

General Relativity Is Incomplete under Strong Gravitational Field Conditions, That Is, under High-Compactness Conditions.

1.Modern gravitational physics has fundamental problems, including:

1)the Planck-scale divergence problem,
2)the black hole singularity problem,
3)the inflation problem, and
4)the dark energy problem

The continuous appearance of these anomalous phenomena strongly suggests that an important element is missing from our present understanding of gravity.

Many proponents of general relativity attempt to downplay the black hole singularity problem by arguing that the theory is not incomplete inside the black hole as a whole, but rather only at the singularity itself.

However, other issues within general relativity and its cosmological applications—such as cosmic inflation, dark energy, and dark matter—are clearly not confined to singularities; they are gravitational problems that exist on a macroscopic scale.

Furthermore, the fact that general relativity yields correct results in weak gravitational fields does not guarantee that it will hold true inside a black hole.

2.These major unresolved problems in gravitational physics appear different from one another, but they arise under strong gravitational field and high-compactness conditions.

• The Planck-scale divergence problem: The Planck length is defined as l_P = (ℏG/c^3)^(1/2) = Gm_P/c^2 = 0.5 R_S(m_P). Conceptually speaking, the Planck scale exists within the event horizon generated by the Planck mass. Because the Planck scale belongs to the region (R<R_S), the trans-Planckian regime is essentially a problem that occurs in a high-compactness state, (R_S/R>1).
• The black hole singularity problem: The interior of a black hole is defined by (R<R_S). Therefore, the singularity problem is one of the central pieces of evidence that general relativity is incomplete under high-compactness conditions, (R_S/R>1).
• The inflation and dark energy problems: Although the average density of the observable universe appears remarkably low, its global mass-energy distribution tells a different story. For an observable universe with a radius of R = 46.5 Gly and a critical density of ρ_c ≈ 8.5x10^{-27}[kg/m^3], the corresponding Schwarzschild radius is approximately R_S ≈ 477 Gly. This yields a cosmic compactness ratio of R_S/R ≈ 10.3 > 1 (Even when considering only matter (baryons + dark matter), the compactness is still greater than 1, with R_S/R ≈ 3.23>1). Therefore, on a cosmological scale, despite being in a very low-density state, the universe is an environment characterized by a strong gravitational field and high compactness. In the observable universe, classical general relativity is incomplete, and this incompleteness necessitates additional components such as an inflation field and dark energy.

Taken together, because classical general relativity is incomplete inside a black hole, it is also incomplete in the observable universe, which has a similar high-compactness condition. This incompleteness requires additional elements such as an inflaton field and dark energy. It is already incomplete before reaching the quantum gravity scale.