# If distant observers never see a black hole form in finite time how can the information paradox be a problem?

So, at least as reported in the media, the physics community is still struggling with the problem of resolving the impossibility of retrieving information from beyond the event horizon of a black hole with the fact that QM seems to guarantee information is preserved.

However, as I understand, a distant observer will never actually see the creation of the black hole occur in finite time. In other words, over all finite times for a distant observer the situation can be described from via solutions to GR that don't actually result in an event horizon in finite time. Now if we assume that either the universe ends after finite time for that distant observer or the (psuedo) black hole evaporates after such time then all events can be described from some perspective without introducing any event horizon.

But by the equivalence principle in GR the perspective of any observer is just as valid and if information is preserved for any observer it is preserved for all observers. So how can there be any confusion?

(The assumption that the universe ends or the (psuedo) black hole evaporates in finite time ensures that there is no observer for whom the external observer's perspective is only valid for a finite amount of time.)

EDIT: Yes, as pointed out the equivalence principle in GR refers to something else. I mean whatever is the GR analog of the SR principle that tells us that a description in any inertial reference frame is equally valid. My understanding was that this was extended in GR to non-inertial observers but regardless of what it is called the point is that if there is any solution of GR that describes all space for all time without the introduction of event horizons then since this description creates no paradox there shouldn't be a paradox with respect to any description.

Also perhaps some assumption about the observer not accelerating to infinite velocity is required as well but maybe such observers are already not considered.

EDIT2: To be more precisce I want to choose a frame whose vector field matches the (usual) local coordinates for some observer who neither falls into a black hole or accelerats to infinite velocity relative to matter in the universe.

Perhaps I am confused and instead want to pick a maximal coordinate chart including all the points on the manifold occupied by my observer.

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Please, please, answer only if you can provide some mathematical reasoning to support your argument. Resist the temptation to answer with what seems to you to be intuitively obvious - GR is rarely obvious or intuitive. – John Rennie Jan 28 '14 at 19:01
The equivalence principle in GR states that one cannot distinguish between a constant gravity field and constant acceleration. – Jim Jan 28 '14 at 19:02
As soon as you talk about comparing things on the black hole horizon to the observations of distant observer, you are no longer talking about a local reference frame. – Jerry Schirmer Jan 28 '14 at 22:35
Sure, but I should still be able to define a (frame)[en.wikipedia.org/wiki/Frame_fields_in_general_relativity] which yields the correct local coordinates. The only importance of the observer far from the black hole who isn't falling in is to ensure that the frame doesn't end up crunching all time for such an observer into a finite period. – Peter Gerdes Jan 29 '14 at 1:16
I think perhaps I mean to say that I should be able to define a coordinate chart that not only includes my observer at all points but also includes all points on the manifold (except perhaps the earliest and last points if they exist) occupied by matter. – Peter Gerdes Jan 29 '14 at 2:11