Time dilation at a black hole

Question

According to the Wikipedia article on black holes:

Even though the collapse takes a finite amount of time from the reference frame of infalling matter, a distant observer sees the infalling material slow and halt just above the event horizon, due to gravitational time dilation. Light from the collapsing material takes longer and longer to reach the observer, with the light emitted just before the event horizon forms delayed an infinite amount of time. Thus the external observer never sees the formation of the event horizon; instead, the collapsing material seems to become dimmer and increasingly red-shifted, eventually fading away.

If this is the case, then why is there a problem about information loss in a black hole? To any observer not inside a black hole, black holes do not exist. Thus there is no problem about information loss. In the same vein, isn't it misleading to say, for instance, that the engines of quasars are black holes? When we observe a quasar, all its mass is still observable in principle (though too red-shifted to see in practice) and no black hole exists.

Answer 1

This has always been a difficult thing for me to understand. The way that I think of it is that although we cannot see past the event horizon, we know that black holes exist due to the properties such as gravitational lensing, which is related to time dilation. This time dilation relates to how we justify not being able to see past the event horizon of a black hole. As far as information loss, it references the matter that the actual black hole body is formed from. The approximate mass and size of a black hole can be measured by different observed properties such as the size of the event horizon and the amount of light shift. Not sure if that really answers your question, but it's how I think of it.

Answer 2

A good question. I think bits of the question have been addressed in various answers hereabouts, but I'm not sure the whole question has been addressed.

The simple answer is that the external observer will (if they wait long enough) see the star start to collapse and then evaporate without ever actually having formed a black hole. The information problem still exists because the information originally contained in the star has been turned into thermal radiation.

The question Will the black hole evaporate in finite time from external observer's perspective? addresses the problem of the evaporation in a finite time, though not in a terribly non-nerd friendly way. Some Googling should find you some more user friendly if less rigorous explanations. Basically the Hawking radiation comes from a region just outside the event horizon (see From where (in space-time) does Hawking radiation originate?), so it radiates away the mass of the star in a finite external time even though the horizon requires an infinite external time to form.