For some reason, physicists are not concerned with information loss via this one. I would be glad if somebody explained the difference.
In both cases it is due to curvature of space, so I think these are essentially the same case.
I would definitely like to hear something verifiable on why there's a difference and why only one of these susceptible to information paradox.
Take that galaxy that just crossed our "observable universe horizon" so that we can't see it. If there is a civilization halfway between Earth and that galaxy, they can still see that galaxy. The galaxy can see that second civilization and so can we. There isn't a single fixed "observable universe" boundary in space, it's just relative to the observer.
With a black hole, it is different. There is no point that can see both sides while being seen from both sides,. If you are outside the black hole, you see nothing from within. If you are inside, then you can see the inside (this is speculation) and you also see the outside. It's a very clear boundary.
This is the direct reason/consequence of not being able to observe the event horizon when near it, or notice when you cross it.
The boundary is not clear, it depends on the observer.
The tl;dr is that if information hides on the other side of an event horizon and doesn't come back, we can pretend unitarity (and all the rest of the physics we've discovered) continues where we can't see it.
A non-evaporating black hole forever holds within it the information about what fell into it.
A forever-expanding universe causes information to exit observability forever.
Partitioning away -- hiding forever -- information is not the same as losing track of it when it comes out of hiding.
There are some differences between these two types of horizon because they are generated by different metrics : one for an expanding spacetime and one for a collapsing one.
We can see the differences by adapting these theoretical (as opposed to astronomically observed) objects.
If an expanding universe's expansion slows and reverses, then eventually all the galaxies that exited from one observer's view return into its view (having evolved with stars forming, aging, dying, galaxies merging, and so forth). If we are talking timescales of a few billion years, then if an us-like observer has detailed information about a galaxy now leaving its view, it can in principle predict what it will look like in billions of years when the galaxy returns back into view. The gentle assumption here is that stellar physics does not stop when the most distant galaxies go out of view.
If the timescale is pushed out to trillions and zillions of years, these us-like observers could still maintain the idea that the galaxies which exited from visibility continue to evolve like the closer galaxies which continue to be seen. A star which ends up on the other side of the cosmological horizon continues being that same star, evolving as normal.
A black hole is different, precisely because we should expect unknown extremely high energy physics to occur as e.g. protons fall in. What happens as you crush some quarks and gluons together at energies enormously higher than that we get from the LHC, or even from supernovae? We don't know. In fact, when we try to answer that, we lose track because our calculations tend to become singular : https://en.wikipedia.org/wiki/Singularity_(mathematics) We don't know what should pop out of a black hole late in evaporation, but we do know when a star crashes through a black hole event horizon, it will stop behaving like a star very quickly.
Indeed, even just on "our" side of the two horizons we can see differences near them. The furthest galaxies, at the edge of what we can see of the cosmos, are filled with normally behaved (young) stars. The shapes of those galaxies are not distorted by proximity to any horizon. We expect that to continue as we see galaxies deeper and deeper into our sky. By comparison we can see gas clouds falling into the black hole in the centre of our galaxy, stars orbiting it, and distortions to these caused by these close approaches to the central black hole. We have even found evidence of stars ripped apart by more distant extragalactic black holes. Crossing a black hole horizon does violence to the bit of the star that has not yet crossed; crossing the cosmological horizon would not change the star's basic behaviour.
If the universe were to collapse in the future, we would expect to see disappeared stars returning into view. Those stars stayed in locally gently curved spacetime, just like our local star did. If a black hole were to shrink in the future, we would be surprised if it spat out intact stars, or space probes, or whatever fell in emerging unscathed. Those objects did not stay in locally gently curved spacetime, and indeed would have encountered the locally enormously curved spacetime inside the black hole. That strong curvature spaghettifies things, at the very least.
These are just the consequences of our best theories of gravitation and matter applied to situations we have no reason to expect to be able to observe. As far as we know our universe is not accelerating towards a recollapse, it is accelerating towards faster expansion. And as far as we know no astrophysical black hole in our universe is presently shrinking. It's fairly safe to bet that if there is ever to be a reversal of the expanding cosmological metric or the collapsing black hole metric it's not going to be soon, so humanity and its descendants have lots of time to think about evaporating black holes (including those that evaporate in a contracting "anti-de Sitter" universe with a big crunch, which is the setting (sometimes including extra spatial dimensions than the three we're used to) for many approaches like the one in the fine article in Quanta Magazine linked at the top).
Now, a more direct answer to your question: in an almost-completely-flat-space universe if we have all the data (position, momentum, particle species, etc) at every point in a time-indexed spatial slice of our universe, we can calculate the entire data in neighbouring slices, and the data in those slices' neighbours, and so forth, into the infinite future and the infinite past. An expanding universe doesn't break this, it just means that we can't choose any arbitrary slice and march forwards and backwards from there, we have to take initial data from the hottest densest earliest part of the universe. From complete initial data and appropriate dynamical laws we can (in principle) describe anything in the future, even if the parts we describe are so separated from one another (in that future) that they can't exchange light with one another. The formation of non-evaporating black holes doesn't change the picture much: we know that things fall into a black hole and stay there in some unknown state, unable to exchange light with things outside the black hole.
However, once we introduce black hole evaporation we have the problem that we don't know how the stuff inside the horizon evolved inside the horizon, so we have no idea what should pop out through the last stages of evaporation.
In our standard cosmology, we can expect black holes to have evolved from stuff that was close to us in the hot big bang era but which is now almost certainly forever outside our cosmological horizon. A general solution to the black hole information paradox should not create craziness in those so-distant-we-will-never-see-them black holes, much less in the earliest visible quasars. That tends to get forgotten until someone asks what the interviewer asked:
Most of the justification for the quantum extremal surface formula comes from studying black holes in “Anti-de Sitter” (AdS) space — saddle-shaped space with an outer boundary. Whereas our universe has approximately flat space, and no boundary. Why should we think that these calculations apply to our universe?
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.
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.
If your "I don't see why it needs introduction of new physics" is a request for information rather than a dismissal of the debate itself, you could start with the late Joe Polchinski's excellent 2013 slide deck https://www.slideshare.net/joepolchinski/firecit and the references at https://en.wikipedia.org/wiki/Firewall_%28physics%29
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.
- --
[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.
[5] For example, https://en.wikipedia.org/wiki/Schwarzschild_geodesics#Geodes... although I'd want to resort to a textbook.
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?
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.
See the section, especially the second and third paragraph at https://en.wikipedia.org/wiki/De_Sitter%E2%80%93Schwarzschil...
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.
- --
[1] https://en.wikipedia.org/wiki/Vaidya_metric#Ingoing_Vaidya_w... (eqn 15 with r ~ 6M).
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.
If I put a log through a wood chipper, I can't un-chip it! Why should we expect the same for stars getting torn apart by intense gravitational fields?
Does it matter that the gravitational field is literally "spacetime itself" changing shape, versus two pieces of matter interacting with each other as in the wood chipper case?
Here's my guess of what's happening based on what you read, please tell me where I'm going wrong:
Physics generally assumes that it can be theoretically un-chipped; if somehow I could run time backwards, that I would end up with exactly the same log that I started with. But the results of interacting with with the mathematical singularity in the black hole cannot be "undone" in this way. And so far, all attempts to avoid trying to model "matter that has passed through a singularity in spacetime" with some kind of firewall, etc. have failed.