First I want to say that black hole does not imply extreme conditions. You will not notice when falling into a really large black hole. They are violent only when small. Large black holes are almost as benigh as outer event horizon, shredding-and-tearing-wise. We can't observe singularity, so whatever matter state it is on has no bearing on information paradox.
With regards of reappearing from black hole. When the universe is close to big crunch, a lot of very heavy black holes begin to merge. When we are virtually inside a black hole, it may merge with more black holes, and if they are sufficiently large, we will be able to interact with objects (such as stars, even) inside the black holes in which they disappeared from our sight previously. Moreover, we will see that they have evolved during their absense in line with how objects outside of observable universe evolved in absense of observation.
This is when talking about very large black holes, the size of our galaxy. These are easier than it sounds due to very fast black hole volume growth.
About evaporation, I can't say too much. But I also don't see how it
UPD:
...I don't see why it needs introduction of new physics, given that it is a virtual phenomenon - nothing interesting really happens near the event horizon, it only becomes interesting at a distance.
Below, I'll focus on model black holes, immersed in vacuum, isolated in asymptotically flat spacetime, and without regard to initial formation.
Yes, you can make such a theoretical black hole arbitrarily large, and thus geodesic deviation[1] can be arbitrarily small just outside the horizon.
The region just outside the horizon[2] is still a strange and likely bad place to be, filled with post-Newtonian effects from gravitational redshift and plunging orbits.
[aside 3]
(Astrophysical black holes must have some upper mass limit, and will generally have accretion structures that produce additional hazards).
> black hole does not imply extreme conditions
I invite you to calculate the scalar curvatures[4] in any model black hole, including one with an arbitrarily high mass (say about that of the known universe), and the geodesic equations below ~ 6(GM)/(c^2) [5]. If you do that, you'll find that extreme conditions are always manifest, and that in particular even for arbitrarily large mass model black holes, once you are past the point of no return you are inevitably drawn into a caustic, and fairly quickly by your own wristwatch-time.
Super-and-ultra-massive black holes are mostly interesting because the curvature very close to the horizon is well within the effective field theory limit of General Relativity, so theorists can be sceptical of the introduction of quantum corrections to gravitation in those regions of (all) theoretical black holes unless the corrections vanish as one takes the black hole mass to a very high limit.
> a lot of very heavy black holes begin to merge
You should consider that clusters galaxies will begin to reappear from the other side of the horizon well before they get close enough to one another to interact gravitationally. The very late time big crunch is not necessary to demonstrate the difference between switching from an expanding universe to a contracting one and switching from a growing black hole to an evaporating one.
Indeed, although late times of black hole evaporation are theoretically interesting (is there a remnant?) even the very earliest stages of evaporation are different: what rushes out from the region around the black hole is greybody radiation, not the stars, rocks, and space probes we threw in while the black hole was still growing.
Taking the mass of a black hole to an arbitrarily large value does not change this essential difference.
I don't know what you're trying to say in the final two paragraphs.
There is nothing virtual about Hawking radiation; it appears pretty generically close to all sorts of black holes equipped with a non-vacuum exterior, and has been shown in acoustic analogues. Unruh: http://inspirehep.net/record/775859?ln=en availabile at https://pos.sissa.it/043/039/pdf If you are perturbed off ISCO by Hawking quanta scattering off you, you likely will care very much that it is not a "virtual" phenomenon, while you are still able to care about anything at all.
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[1] We can consider the Riemann curvature tensor R^{a}{}_{bcd} u^b u^d X^c, where u^a is the 4-velocity of an object on a geodesic and X is a vector quantity in the tangent space between that geodesic and one nearby (e.g., a different mote of neutral dust in an infalling cloud, with identical 4-velocity) describing these geodesics' tendency to separate or converge. More roughly, this encodes the inwards-squash and the back-to-front stretch of this dust cloud from a macroscopic perspective. It also, in suitable coordinates, describes the spaghettification of extended bodies bound by non-gravitational forces. For spherically symmetric masses, in general X shrinks with distance from the mass. For black holes we take the mass to be highly focused so this obtains practically everywhere in the Schwarzschild interior. The interior oddities arising from breaking the symmetries of Schwarzschild with e.g. a non-negligible spin parameter do not change this statement qualitatively.
[2] In the Schwarzschild case the region R_s < r < ~ 3R_s is prone to result in inward plunges for non-massless objects, and of course the size of that region scales with M. Some details: https://hepweb.ucsd.edu/ph110b/110b_notes/node80.html Less symmetrical black hole models also have exterior regions, scaling with M, that are hazardous to any non-massless observer.
[3] The region just outside the cosmological horizon is essentially identical to the region just inside the cosmological horizon. There is an important symmetry difference: when someone else recedes past our cosmological horizon, we recede past theirs. We do not notice when we exit someone else's cosmological horizon -- we are doing it right now. We continue on diverging geodesics (cf [1]). Being on the inside of a black hole -- even one with a mass greater than the observable universe -- gives a different view. With the time one has left, one could determine (via e.g. Synge's method) that the spacelike part of the spacetime curvature is curved and thus one is inside a truly enormous vacuum black hole. If we break the vacuum condition Robertson-Walker -> Friedmann-Lemaître-Robertson-Walker & vacuum Schwarzscild -> Lemaître-Tolman-Bondi, we would not see isotropic distance-dependent gravitational redshift of luminous matter inside the LTB black hole as we do in the FLRW expanding universe: there would be an enormous anisotropy.
[4] Let's use Schwarzschild (black hole and coordinates) to avoid drowning in calculations for a black hole equipped with an "outer event horizon"; the interior metric is also much easier to reason about, and compared to cases such as Kerr-Newman, much more physically plausible. For a Schwarzschild black hole, the Kretschmann curvature scalar is R_{\mu\nu\lambda\rho} R^{\mu\nu\lambda\rho} = \frac{48M^2}{r^6}, where R is the Riemann curvature tensor. Coupled with the appearance at r = 2M of the Schwarzschild horizon, we can see that as we take M -> \infty your point about "benig[n] ... shredding-and-tearing-wise" holds. However, calculating for the interior, we find that the Kretschmann scalar explodes and becomes irregular at r = 0. This is diagnostic of a gravitational singularity.
Trying to orbit a black hole near the horizon is a bad idea indeed, since most of observable universe's light will be blueshifted to high energy X- and gamma rays in my understanding. But, freefalling into a large black hole should not be inherently dangerous, because you are blueshifted in the same fashion as light, travelling at very high speed at this point, so I don't expect you to be roasted. I admit that it's very hard to freefall into a black hole, because any angular moment around black hole will be conserved, and you have great chance to near-miss it and be grilled as you fly away from the event horizon. But it should be simpler with larger holes.
Black hole evaporation is basically nonexistent for any large black hole. It is theoretically puzzling, but not something you would interact with when falling into event horizon. Since you will never observe crossing event horizon, you also have no chance of having close encounter with (already very feeble) evaporation radiation. You will just see it happening elsewhere, at any moment.
As soon as you have crossed, the direction to center of mass is your new time axis, so you won't directly experience movement towards it. If the black hole is really large, you can spend some time in it, and then interact with other observers who were unreachable for you, but now they are since they have also entered this black hole, or have entered another black hole which then merged with that of yours.
Can you please elaborate on the point [3]? How does one determine that they are in the universe-sized black hole? What difference would it make?
In a vacuum solution, there is no "observable universe's light", there is only the central mass M at point p, and some test observer who can probe point != p.
If there is starlight falling onto the black hole we adapt the metric e.g. Schwarzschild -> Vaiyda (incoming) [1], which models this incoming light as spherically symmetrical, ignoring Olber's paradox, and equipped with no wavelength, charge, or rest-mass: a "null dust". The major practical difference is on the wavelength stretching/squashing that light would experience, but the "null dust" does end up with lighter or heavier "raindrops". In this approach, and more realistic but still very theoretical ones, there are families of accelerated observers, including ones orbiting at ISCO, that will be trying to move through a torrent of heavy-raindrop incoming null dust.
"Freefalling into a large black hole should not be inherently dangerous". No, a massive radial freefaller in the Vaiyda model will get splatted on the back windscreen by heavy raindrops. More physically, a subluminal radial infaller will get sunburned by distant starlight trying to race past it, and additionally any other faster-moving infalling mass, such as cosmic ray protons.
"It's very hard to freefall into a black hole". One can do brief course corrections as one approaches the black hole, and still be in freefall when one shuts off the short-impulse thrusters. The adaptation of the resulting worldline isn't especially hard, and one can simply take its cutoff at the final course-correction. This is easy enough to see with a Minkowski diagram -- the accelerated parts of the worldline will be curved, the freely falling parts will be straight-lined: this image is frequently encountered in resolutions to the Twin Paradox where physically plausible acceleration is introduced.
> evaporation is basically nonexistent for any large black hole
In a theoretical model, like Schwarzschild, we literally have all eternity to trace the black hole's evolution, of course. The central finding of Hawking's 1974 paper is that arbitrarily large Schwarzschild black holes with vacuum (or classical electrovacuum) substituted with a noninteracting scalar quantum field will evaporate in finite (if long) time. Follow-on work has generalized to different quantum fields and black holes that form by collapse or which have non-negligible spin or charge parameters.
More astrophysically, we do expect to find Hawking greybody radiation around black holes of all sizes in our universe. The greybody temperature will be cold, especially for more massive black holes. Crucially this temperature is much less than that of the cosmic microwave background (much less typical interstellar or intergalactic-but-in-cluster media), so the Hawking radiation cannot cause these black holes to shrink. The origin of the Hawking quanta extends well outside the event horizon, so a well-planned hyperbolic orbit with well-shielded and sensitive sensors should pick them out. There are plausible natural phenomena which that idea roughly models, or conversely, it could be revealed by the inverse compton scattering spectrum of a very large weakly-feeding black hole (Sgr A* is not hopelessly far from that!).
I'm sorry, I just can't understand what you are trying to say in your second paragraph's second sentence. (The first sentence is just observing that collision with the singularity is in the future of every object crossing the horizon. "Time axis" depends on choice of system of coordinates, and one has total freedom there (including using no coordinates at all), as in any General Relativity problem. I don't see how to relate that to other infallers though. "Everyone gets squashed into the singularity" is what you are trying to say? So? It's not like one can have a conversation when one is part of a singularity.)
> How does one determine they are in the universe-sized black hole?
One looks at the sky and sees everything in it apparently contracted to an extremely bright high-energy point. If one sees a spread of galaxies occupying different solid angles on practically the entire sky, with smaller angles relating to higher redshift, one is not in a black hole, one is in an expanding universe.
In a vacuum setting, where there are no galaxies at all, one would have to measure the local spacetime curvature as discussed in https://physics.stackexchange.com/questions/109731/how-to-me... -- particularly the overview of the point raised by JL Synge in his textbook 1960 Relativity: The General Theory; Pub: North-Holland that one finds in one of the upvoted answers. As noted in several of the answers, with some care one can measure an angle deficit. Alternatively one could track the evolution of a freely-falling spherical dust cloud's oblateness/prolateness: https://math.ucr.edu/home/baez/gr/ricci.weyl.html -- in a vacuum expanding spacetime sphericity would be maintained, whereas in a vacuum black hole the cloud would become ellipsoidal. Even in a universe-sized black hole, starting far from the singularity, the cloud would on human timescales develop a "nose" pointing in the direction of the singularity.
> What difference would it make?
The interior of a universe-sized black hole is not compatible with life (or star formation).
(Life (and stars and galaxies and so forth) could in principle exist outside a universe-sized black hole, but would notice that the views towards the black hole and away from it differ remarkably).
Why does this matter? It addresses your point that a universe "close to big crunch, a lot of very heavy black holes begin to merge" is an objection to stars and galaxies popping into view after than had receded behind a cosmological horizon, which also sidestepped the point that as a black hole horizon recedes, stars and spaceprobes and so forth do not pop out.
Black holes and cosmological horizons are just different.
We got to this difference by you rejecting isk517's perfectly reasonable comment, "Things moving super far away are lost but should still be out there, things falling into a black hole disappear and then once the black hole evaporates are gone forever", which I have just been expanding upon. In particular your objection was "In both cases it is due to curvature of space, so I think these are essentially the same case". Above is how they are not the same case, stemming from the curvatures of black holes and expanding universes having different sign. Finally, you asked to "hear something verifiable on why there's a difference and why only one of these is susceptible to information paradox". Which I was trying to do. The tl;dr is that the contents of a black hole drives Hawking radiation even if the radiation's associated greybody temperature is too cold for evaporation; the expanding universe's contents cools and when the associated ~blackbody temperatures drop below that of the Hawking radiation, black holes will fully evaporate. That evaporating black holes have a greybody spectrum unrelated to the microscopic details of what fell in is the information loss problem in a nutshell.
Thank you for deciphering my thoughts and then trying to reason in the same context.
With regards to heavy raindrops, it is very interesting if we can quantify this effect.
For example, let's imagine that you are falling into a black hole with Schwarzschild radius of 200,000 ly, which is located between Milky Way and Andromeda galaxy, and there's no huge accretion disk on this black hole (let's imagine we're falling at 45° tilt to its equator and with zero angular momentum WRT its spin, but we can also imagine a non-rotating black hole with no accretion happening at all). We are at 1.1r. What's the energy flux due to heavy raindrops? What's the energy flux due to Hawking radiation escaping? While I don't expect you to do the math, and I did not, my common sense tells me that latter is "negligible" and former is "significant, but not something you can't realistically shield against". Do you happen to appraise it differently? Otherwise, it seems that we are able to enter the sufficiently large black hole as an outside observer.
Then, I would expect that we would see the other stuff falling into the black hole in proximity with our own point of entry (entire stars even), and I expect that they will be somewhat blue shifted. Imagine a star which has fallen in this black hole at the same time as our observer, on a distance of 2 ly. We have at least 200,000 years before we hit the singularity to make observations. After 100,000 years we will observe that the star is only 1 ly away, which translates into 1/100,000 blue shift of that star towards the observer. I also don't immediately see why everything we see inside this black hole will be contracted to an extremely bright point. Maybe the "outside universe"'s light would? The light from other objects inside this Schwarzschild radius (which has not hit the singularity yet) should be propagated normally, with slight blue shift. Clouds developing a nose may be a thing. However, in no way they the nose can point towards the singularity, since the singularity (the center of mass) will literally be in the future, the 𝛕 axis pointing towards it. So the whole cloud will move in the direction of the center of mass with almost speed of light. This is how we will perceive it locally, of course.
Now we are returning to information paradox and black hole evaporation. Here, we have Kruskal–Szekeres coordinates which allow us to describe precisely what happens when matter falls into a black hole, and this includes the Hawkins radiation pairs. As a layman, I see these holographic solutions of information paradox, at best, an example of explaining the black hole evolution while working in bad coordinates (the ones tied to us as an observer), and at worst a result of further confusion. Kruskal–Szekeres coordinates also have "time axis" which you have previously dismissed.
My point is that nothing special happens in "our" coordinates, nothing special happens in the coordinates set inside the black hole, and nothing special happens with the observer which is freefalling into the black hole, so there is no case for information paradox other that information travelling through the event horizon.
Maybe there is some sort of paradox of matter falling into singularity, but it is entirely unrelated to event horizon, a distinct phenomenon. In this fashion, it can't be used in explainations of black hole evaporation.
> The interior of a universe-sized black hole is not compatible with life (or star formation).
It is a very bold claim, but I wonder what happens with life which has just entered the universe-sized black hole, with sufficient shielding to survive it of course. How long does it have and what will affect the outcome? Same with pre-existing stars.
If they still have some runway, then you can surely observe the scenario when object A falls in a black hole outside of observability by B, then B falls into another black hole, then black holes merge and with some luck, A and B are observable to each other. But even if they don't, it's not important since observability is not a function of life or stars, in my understanding it just means that two objects can interact, and some kind of objects (if just protons or quarks) should be possible inside the black hole.
I don't claim that black hole equals cosmological horizon, I'm just imagining that they're the same with regards to the (absense of) information paradox.
I imagine that a computation-intensive simulation involving the outside of black hole, the inside of black hole and how they evolve and interact with regards to coordinate translations may shed some light on how the black hole evaporation works, without any additional physics such as holographic surfaces. And the solution will probably not lose information at any point. It's just that there is no observer to whom the whole information is available at any point of the evolution.
I'm sorry that while I have typed a lot of things, they're not in the direct coherence with your arguments, which, in time, were not in direct coherence with my previous point, so we are bound to zigzag.
First I want to say that black hole does not imply extreme conditions. You will not notice when falling into a really large black hole. They are violent only when small. Large black holes are almost as benigh as outer event horizon, shredding-and-tearing-wise. We can't observe singularity, so whatever matter state it is on has no bearing on information paradox.
With regards of reappearing from black hole. When the universe is close to big crunch, a lot of very heavy black holes begin to merge. When we are virtually inside a black hole, it may merge with more black holes, and if they are sufficiently large, we will be able to interact with objects (such as stars, even) inside the black holes in which they disappeared from our sight previously. Moreover, we will see that they have evolved during their absense in line with how objects outside of observable universe evolved in absense of observation.
This is when talking about very large black holes, the size of our galaxy. These are easier than it sounds due to very fast black hole volume growth.
About evaporation, I can't say too much. But I also don't see how it
UPD: ...I don't see why it needs introduction of new physics, given that it is a virtual phenomenon - nothing interesting really happens near the event horizon, it only becomes interesting at a distance.