# 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: