Are Black Holes Proven or Just Theoretical Constructs?

[Drakkith]

I just thought of this. If the Big Crunch could compactify spacetime into a singularity (or at least near Planck scale pending quantum gravity). Why don't the black holes in our universe compactify the spacetime inside the event horizon into the singularity (in other words, making spacetime inside the event horizon just vanish by sucking into the singularity just like what Big Crunch could theoretically do)?

A big crunch is not believed to be a possibility given that the expansion of the universe is accelerating. What goes on behind the event horizon of a black hole is unknown at this time, however I would guess that it is reasonable to assume that spacetime doesn't "vanish" behind the event horizon. I don't even know what this really means of the implications of it.

 

[Markus Hanke]

A big crunch is not believed to be a possibility given that the expansion of the universe is accelerating. What goes on behind the event horizon of a black hole is unknown at this time, however I would guess that it is reasonable to assume that spacetime doesn't "vanish" behind the event horizon. I don't even know what this really means of the implications of it.

Spacetime does not just vanish inside an event horizon. What happens rather is that space-time ceases to be a smooth manifold due to quantum fluctuations. In practical terms this would mean that the distance between two given points ( points in space or points in time, or both ) on the manifold can no longer be well defined; points in such a space-time may no longer be causally connected. What such a space-time would look like for an observer traveling through it...well I leave that to your imagination. Let's just say it wouldn't be a pleasant experience. The point of singularity itself would likely never be reached, because there simply is no meaningful way to define such a point in a non-connected manifold in terms of spatial coordinates. After all, how do you tell if you have reached the singularity if the notion of distance is no longer well defined ?
As an observer continues to fall inwards ( with reference to the event horizon he has just crossed ) the classical concepts of up-down, forward-backward, left-right, before-after, become more and more meaningless. What happens to classical matter and its constituents at this point is not entirely clear to me; it would seem that due to the fluctuations of the space-time background the forces binding the elementary particles into composite particles would cease to function in their normal manner. Basically all matter will eventually break down into its very basic constituents, whatever these are ( vibrating strings ? ). I picture a singularity therefore as a chaotic quantum foam of energy, which is neither point-like nor does it have a spatial volume that can be defined in any meaningful way; however, it is obvious that the total energy bound in this system must be finite. How this could be defined in the absence of a smooth space-time, however, is up for speculation. Even very basic attributes like dimension and topology are no longer definable in this picture.
A much clearer idea of all this should emerge with a consistent theory of quantum gravity.