## 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:

## Comments

## Bertrand Le Roy said:

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:

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.

## Adi Oltean said:

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:

## Bertrand Le Roy said:

## Bertrand Le Roy said: