# Black hole evaporation paradox?

I just sent this letter to Scientific American. I'd be interested to have any informed opinion on the matter.

I’ve read the article about black hole computers with great interest, but there are still a few questions that I think remain unanswered.

The article makes it quite clear how black holes could be memory devices with unique properties, but I didn’t quite understand what kind of logical operations they could perform on the data.

But another, more fundamental question is bugging me ever since I read the article. From what I remember learning about black holes, if you are an observer outside the black hole, you will see objects falling into the black hole in asymptotically slow motion. The light coming from them will have to overcome a greater and greater gravitational potential as the object approaches the horizon, losing energy along the way and shifting to the red end of the spectrum. From our vantage point, it seems like the object does not reach the horizon in a finite time.

From a frame that moves with the object, though, it takes finite time to cross the horizon.

This is all very well and consistent so far. Enter black hole evaporation.

From our external vantage point, a sufficiently small black hole would evaporate over a finite period of time. So how do we reconcile this with the perception that objects never actually enter the horizon?

It seems like what would really happen is that as the horizon would actually become smaller over time, the incoming particles would actually never enter it.

If this is true, and no matter ever enters it, would the black hole and the horizon exist at all?

From the point of view of an incoming object, wouldn’t the horizon seem to recess exponentially fast and disappear before it is reached?

If nothing ever enters the horizon, is it really a surprise that black hole evaporation conserves the amount of information?

Does the rate of incoming matter modify the destiny of the black hole? If it grows faster than it evaporates, I suppose the scenario is modified, but how so?

I know it is quite naïve to think in these terms and that a real response could only come from actual calculations, but still, I hope that you can give me an answer to what looks like a paradox to me. I don’t see how you can reconcile the perceptions of an external and a free-falling frame of reference if the black hole evaporates except if nothing ever enters the horizon.

**UPDATE:** a recent paper presents a similar theory to solve the information paradox:

http://arxiv.org/abs/gr-qc/0609024v3

http://arstechnica.com/news.ars/post/20070622-apotential-solution-to-the-black-hole-information-loss-paradox.html

## Adi Oltean said

Black hole evaporation is a real effect. The speed of evaporation is directly related with the mass of the black hole. Very small black holes are dying very quickly. Larger black holes have a much larger evaporation time. In general, the speed of evaporation is proportional with the cube of the black hole mass. Here are more details on this subject: http://en.wikipedia.org/wiki/Black_hole_evaporation

## Bertrand Le Roy said

Sure it's a real effect, but it sure isn't yet a fully understood phenomenon as it lies at the frontiers of quantum mechanics and general relativity, which, to say the least, don't mix well. Thanks for the link, which is very informative and should give a basic understanding of the phenomenon to those who don't know about it. An important piece of data in this article is the time it takes a black hole to evaporate. Black holes formed from a collapsed star seem to have no chance of disappearing anytime soon, or anytime at all. Only primordial black holes (formed at the same time as the universe) could evaporate in a reasonable amount of time. Furthermore, the article says that the equilibirum size for a black hole (where it absorbs as much as it emits) would have the mass of the Moon. Again, primordial black hole only. Unfortunately, no one knows if small primordial black holes exist. We have some clues about large primordial black holes, but so far not small ones, as far as I know. Anyway, my main point was what happens really to a particle that plunges into an evaporating black hole? Does it enter the horizon at all?

## Adi Oltean said

>>> Only primordial black holes (formed at the same time as the universe) could evaporate in a reasonable amount of time. This is not known yet.... At least in theory, small black holes are continously forming and dying quickly all the time. All you need is enough energy to "compress" matter in a very small area. Given enough energy, this is possible. It is suspected that cosmic rays (that have extremely high energies, above hundreds of MeV) can create these black holes. Fortunately, these black holes are dissapearing as quickly as they are created so there is no danger there. See this link for more details: http://www.newscientist.com/article.ns?id=dn4446 >> Anyway, my main point was what happens really to a particle that plunges into an evaporating black hole? Does it enter the horizon at all? Of course. There is nothing special about this horizon, except that anything that goes there cannot come back. This might look weird, but it is not completely weird to have movement only in one direction in the four dimensional space-time. Actually, in space-time, this is a natural property of the time dimension - things are only moving one way, from past to future. With space dimensions, things can move both ways except in the case of black holes, when they move only in one direction.

## Bertrand Le Roy said

Adi, thanks again for the feedback. I didn't know that mini-black-hole could form so easily, I thought stellar and primordial were the only kinds. I guess my physics are a little outdated (I quit the field ten years ago). But now that I've read the article, it sure makes sense. Now, on the second point, of course I'm not discussing the possibility that a particle can theoretically enter a classical horizon. I used to know General Relativity quite well having worked in a Cosmology laboratory during my PhD thesis so this is quite clear to me, no mystery there. The particle enters the horizon in finite time, we just perceive that it takes infinitely long and it's ok because our region of space-time is causally diconnected from the inside of the horizon so there's no paradox. What I'm talking about here is very different. When a black hole evaporates, from our reference frame, we see incoming particles taking infinitely long to cross the horizon. At the same time, we see the horizon recess and finally disappear. So a logical conclusion seems to be that from our reference frame, we still see the particle after the black hole has disappeared, and it never entered the horizon. But there is only one objective reality even in Relativity, so the only conclusion seems to be that the particle never enters the horizon. From the reference frame of the particle, what must happen is that events seem to happen faster and faster, including the recession of the horizon and its disappearance in finite time. I think no particle ever enters the horizon of an evaporating black hole. Which gives a different answer to the information paradox. That's my point. I'm very ready to be proven wrong, I'd be more than happy to: I'd learn something new, and I just love that.

## Adi Oltean said

Oh, I see now your original point. Interesting problem... So, let me dumbify a little the experiment so I can understand it... :-). A source of light is launched from some point outside of the black hole. The source approaches the event horizon and enters into it. From an external point of view, photons will be continuously detected with lower and lower energies. Now here comes BH evaporation. At some detectable point in future (around t1 in the reference frame of the observer) the black hole completely evaporates. At this point in time (or around it) the source of the signal simply stops from the observer point of view. For sure, something happened with that source of light due to the interaction with the black hole. But I think that the end result should be that the observer must have NO way to determine whether the source already entered or not into the event horizon. Anyway, all these are simply speculations which might or might not make any sense given that I am not familiar with the mathematics around this theory. Probably the event horizon becomes "special" when the black hole is near to its end of life and close to quantum dimensions? This special "fuzzy" event horizon will look like it is triggering other physical interactions which might cause the destruction of the source of light due to the black hole. And these interactions must also give the same end result to the observer as in the case when the source actually entered into the black hole, and the BH died shortly after that.

## Bertrand Le Roy said

I disagree with this interpretation. From our reference frame, the very moment when the object crosses the horizon is infinitely distant in the future, even though from its own reference frame, what seems infinite to us is actually finite for it. It's not just photons being detected with lower energies. If you compare the two events (the moment the black hole evaporates and the moment the particle should enter the horizon - if it still exists -), their succession is clear: one happens in finite time, not the other. Thus, it is clear that the object enters the horizon after the latter has disappeared if at all. Any physically relevant coordinate transformation will maintain the order of these two events as they happen at the same place. So the horizon must recess before the particle enters it. Your hypothesis that something "happened" to the object which results in it being inobservable after the black hole has collapsed does not seem to be backed by any necessity or evidence (I know, we're speculating here anyway). But I think my hypothesis is backed by the fact that it does not rely on any new or mysterious phenomenon - no deus ex machina - and is consistent as far as I can see. There is no problem with the object not seeing the horizon recess (no object can see the horizon itself anyway). I think you're right in saying that the actual disappearance of the black hole is pure speculation as we don't know the pysics of this scale, but we don't need to wait for that moment. Even when the final moment of evaporation is still far in the future, I think we can see that the horizon recesses faster than the particle approaches it from the arguments above. Except of course if I'm overlooking some phenomenon or if my understanding of the evaporation of black holes is too naïve to be of any use. But I'm really curious to see the advice of specialists of the field.

## TrackBack said

## Adi Oltean said

>>> If you compare the two events (the moment the black hole evaporates and the moment the particle should enter the horizon - if it still exists -), their succession is clear: one happens in finite time, not the other. Thus, it is clear that the object enters the horizon after the latter has disappeared if at all. Well, my assumption was that the dissapearance of a black hole is an observable event (as predicted by theory when the mass of a black hole is extremely small), In this case, we can safely assume that some objects entered into it shortly before that event... ... If there is such thing as a black hole with a finite lifetime from our reference frame.

## Bertrand Le Roy said

Sure it's observable. Actually, that's kind of my point. How does that make it safe to assume that some object entered it (other than virtual particles created from the vacuum in the immediate vicinity of the black hole, whose information content is doubtful at best)?

## Myself said

"Nevertheless, many climate researchers have been unable to explain why evaporation figures have decreased in areas where rainfall and cloudiness have become more prevalent. If less water vapor is moving into the atmosphere, how could more rain and clouds be forming?" The above comments was witdrawn from a CNN report on the evaporation "paradox". However, there is no paradox as well as there are no other paradoxes in this area, and the CORRECT AND REAL solution to these questions you find in http://noparadoxes.tripod.com. These "paradoxes" appeared only due to the lack of a suitable background on the evaporation and atmospheric processes. That is really THE solution.

## Bertrand Le Roy said

"Myself": what does this have to do with black hole evaporation???

## Tooky said

This stuff is all so cool. Im 14 and wish to go into this field later on. Is there any such thing as a worm hole? i dont think there is but if there is what is it??

## Bertrand Le Roy said

Tooky: wormholes are a theoretical possibility in many cosmological models but nothing has been observed so far. They are connections between parts of a spacetime that are otherwise remote in time and/or space. Imagine cutting two holes in a sheet of paper and gluing them together. If you had to travel from the place where one hole is to the other, if the holes weren't there you'd need to follow a path on the sheet. Now, with the holes, you can travel instantly from one place to the other. Furthermore, you could even theoretically travel to otherwise inaccessible places like the past. It's a shortcut in spacetime, if you want.