Black holes & hawking radiation

[Denton]

So we have an object falling into a black hole. By its perspective it falls in real time, and by the perspective of the outside it never reaches the event horison. Now if black holes slowly evaporate due to hawking radiation, if one were to observe the black hole for countless billions of years till its mass had radiated away, would the object that attempted to reach the black hole be inside or would it still be out?

 

[La Guinee]

I don't know the answer to this question. Here's what I do know. We on the outside never see it cross the event horizon. However, in the frame of the particle, it does in fact cross the event horizon with no problem. And of course, once it does, it's doomed. You can calculate the amount of proper time it takes to reach the singularity once it crosses the event horizon, and it's pretty quick. Much quicker than billions of years. But that still leaves the question of how to reconcile this with the fact that we never see it cross the event horizon. My guess is that on the outside, we will continue to see it asymptotically approach the event horizon even after the black hole is no longer there. But, like I said, I don't really know.

 

[spidey]

So we have an object falling into a black hole. By its perspective it falls in real time, and by the perspective of the outside it never reaches the event horison. Now if black holes slowly evaporate due to hawking radiation, if one were to observe the black hole for countless billions of years till its mass had radiated away, would the object that attempted to reach the black hole be inside or would it still be out?

I think,after some time, black hole won't be there and hence no event horizon...Moreover, black hole radiation is not yet observed...

 

[Naty1]

In a local frame, the object crosses the event horizon, disappears, and is torn apart as it approaches what is believed to be a singularity or immense gravitational strength. The Hawking radiation that is emitted appears to be black body type, random radiation which does not appear to carry any signature of all the "stuff" which has crossed the event horizon...the exact fate of information I believe is still a matter of debate but Hawking has relented on his original belief that all information is lost forver...

As you noted, it is only from an outside stationary observer frame of reference that the object appears to never reach the event horizon; a free falling observer would see the object disappear across the event horizon...

I would say the object falls in "local" rather than "real" time as there is no "real" time upon which all observers can agree...

 

[Denton]

Yes but my question was, when the black hole evaporates to a state in which i does not have an event horsion anymore (aka not a black hole), from the perspective of the outside witness does the object make it in, or is it saved or somehow both?

 

[Naty1]

and by the perspective of the outside it never reaches the event horison.

You answered your own question...and I restated that in my post...

 

[George Jones]

Consider two observers, observer A that falls across the the event horizon and observer B that hovers at a finite "distance" above the event horizon, and two types of black holes, a classical black hole that doesn't emit Hawking radiation and a semi-classical black hole that does.

For the classical black hole case, B "sees" A on the event horizon at infinite future time, and B never sees the singularity.

For the semi-classical black hole case, at some *finite* time B simultaneously "sees": A on the event horizon; the singularity. In other words, the singularity becomes naked, and A winks out of existence at some finite time in the future for B.

In both cases, B, does not see (even at infinite future time) A inside the event horizon, as this view is blocked by the singularity.

These conclusions can be deduced from Penrose diagrams, FIGURE 5.17 and FIGURE 9.3 in Carroll's text, and Fig. 12.2 and Fig, 14.4 in Wald's text.

 

[Naty1]

I like George's answer as well...

if the original questions implies a paradox ,well yes there is..just as there is when two observers moving relative to each other see the other guy's clock slower than their own...and wave particle duality...

An observers frame of reference is all important, as a measurement technique appearing to determine an outcome.

It's not a simplistic world out there...

 

[Denton]

You answered your own question...and I restated that in my post...

How? All you said was that the local observer would fall into the black hole and the outside observer would never see it cross the event horison. Thats all you defined.

When the black hole evaporates to a state in which it does not have an event horison anymore, the observer MUST see one thing or the other. So which is it, the object is inside the now deceased black hole or did it never cross it at all.

If there is a paradox there, then somethings wrong. This is not an impossible scenario.

 

[Jonathan Scott]

How? All you said was that the local observer would fall into the black hole and the outside observer would never see it cross the event horison. Thats all you defined.

When the black hole evaporates to a state in which it does not have an event horison anymore, the observer MUST see one thing or the other. So which is it, the object is inside the now deceased black hole or did it never cross it at all.

If there is a paradox there, then somethings wrong. This is not an impossible scenario.

According to the coordinate time the falling object does not cross the event horizon in finite time, so if the black hole goes away in finite time, that happens first. That's what you said before, and it is not a paradox. Note that if the black hole goes away, the event horizon shrinks down as it does so.

 

[Naty1]

and by the perspective of the outside it never reaches the event horison

Jonathan's answer and my answer are as clear as your quote above...but you have to read all posts on relativity very carefully...this stuff is not obvious, our posts are not edited for clarity so wording may be unintentionally ambiguous, and (gasp) sometimes posters make mistakes...

There could be some ambiguity/uncertainty in how the final events unfold since if the black hole finally evaporated via gradual radiation and smoothly and continuously disappeared, the weakening gravitational field eventually would weaken and the event horizon disappear. ...but from what little I have read about the final theoretical end of a black hole, I don't think they end quite so smoothly...some have postulated explosions akin to collapsing stars...but I do not know the final mechanism.