skeptic2 said:
Correction not a collapsing spherical universe inside but rather a collapsing, sort of conical universe.
Actually the shape of the local universe becomes (hyper)tubular, \mathbb{R}\times \mathbb{S}^2 with circumferential radius shrinking to zero in finite time. And yes you can sort of say all matter inside the event horizon is "simultaneous" but it isn't meaningful.
Visualize it this way. Imagine a string of observers infalling into a black hole. As they approach the event horizon the surface will seem to stretch flat and as an observer crosses he will see the universe as a hyper-tube, with cross section the circumferential two sphere and extensive forward and backward direction seemingly spatially flat. Observers entering before him will be ahead of him and those who enter later will be behind him. They will accelerate away from each other due to tidal gravitation along the length of the tube. Each observer will also experience a tidal force growing over time.
If it were not for the shrinking radius he would be able to move laterally "completely around the universe" returning back were he started (equivalent to circumnavigating the black hole) and indeed observers entering at different angles will be displaced laterally w.r.t. each other. I think eventually there would be event horizons fore and aft growing nearer as time passes due to increasing tidal acceleration along this z axis. Eventually the radius will decrease squishing the observer laterally against himself while tidal forces rip him apart in the fore and aft directions. The singularity will be when the "tube" shrinks to a line.
Schwarzschild metrics are:
d\tau^2 = \left(1-\frac{R}{r}\right)dt^2 - \left(1-\frac{R}{r}\right)^{-1}dr^2 - r^2 d\Omega_2^2
which I pluralize because of the coordinate discontinuity at the r=R event horizon so we have two metrics one inside and one outside. (Omega here is the unit sphere coordinates and d Omega^2 the unit sphere metric.)
Recall that r is defined here as the circumferential radius and for the interior metric r<R this parameter is time-like. The parameter t becomes space-like so it is associated with time only formally. Now given this I would relabel t->z and r->-T and rewrite the metric as:
d\tau^2 =\frac{|T|}{R+T}dT^2 -|T|^{-1}\left(R+T\right)dz^2 - T^2 d\Omega^2
(Note: T is negative r so T increases in the forward time direction. I put in |T| so the signs of metric terms would be clear but |T|=-T = r.)
We can "normalize" the time coordinate with suitable reparameterization t = f(T) so that...
(pardon me for reusing variable names but bear with me...)
d\tau^2 = dt^2 - a(t)^2dz^2 - r^2(t)d\Omega^2
It is not proper to call the inner Schwarzschild solution "stationary" since the metric depends there on a time-like parameter
r=T=f^{-1}(t).
It is then clear that you here have a z-axis by 2-sphere spatial component (hyper tube) with time varying but not spatially varying metric (unless you add in the effects of the infalling masses) with the radius going to zero as t approaches some limit value which further analysis will show is finite.
Now of course other coordinate systems make clearer the continuity across the event horizon but I think this analysis give the best intuitive grasp of what is going on inside. We think of hitting the singularity as an impact. What one would experience is a time at which our local universe shrinks down and stretches out into a straight line. One never runs into the original matter which formed the black hole or any matter which fell in earlier or later if you aren't real close to it in both time and point on the event horizon when you cross. Eventually the tidal forces will pull any earlier in-falling object out of reach (beyond tidal acceleration horizons fore and aft).
I'm not as clear on whether this line can be considered to exist beyond the crunch event at r=0. Essentially time stops locally in the same sense that time begins at the big-bang event.
This is a little bit tangential to the OP but I hope instructive.
