Is all of a black hole's mass situated arbitrarily close to the event horizon? Forgive me if I'm thinking about black holes in completely the wrong way, but since time dilation increases to arbitrarily large amounts the closer you get to the event horizon of a black hole, wouldn't that make it impossible for anything to cross it, since it would require an infinite amount of time?
Is every single black hole in existence just an infinitely thin sphere of infinitely red-shifting matter around some kind of physics-breaking empty space that we'll never know anything about because it's impossible to get to? And if that's the case, does the "singularity" at the center of a black hole actually exist, or is it just a center of mass?  
 A: You are wrong about the empty space part.
Sure you could make a black hole like that by taking a spherical shell of matter and letting it collapse around an empty space until it starts to get really close to the limiting event horizon.
But that's not normally how it happens. Normally you have something like a neutron star that already has matter in the inside, all the way down, even at the center.
So there is matter on the inside and the outside and every place in between. And there is a moment/event when the event horizon forms at the center and starts to rush out at the speed of light.
And that moment is a moment you don't see if you don't cross the horizon.
So you see the parts in the center from before that moment. And you see the parts on the outside from before the moment that expanding event horizon gets to them. And same with the parts in the middle, you see the moments before the event horizon got to those parts.
So you see every part of the star, you don't have a missing part. It is a frozen star or a red star. You see the center and the rest, but in very slow motion and very red shifted.
Now since the outer part of the neutron star blocked your view of the inside long before it formed a black whole, that is the reason you can't see the center. If you'd somehow put in a well with strong walls that let you see the center then you'd be able to look through it but it would be a slow and red view.
A: From what I know of black holes, you may get a few theories from this question, but the truth is we don't know presently.  Singularities such as this are complete mysteries.  We may never know, but as long as we survive our own  self destruction, I believe we will figure it out eventually. :)  
