Gravity is caused by the warping of space-time. Under normal circumstances, it is the time component of the warping that is the most significant. This shows up, for instance, with atomic clocks, which run slower deeper in a gravity well.
Rulers, though, are also affected by bravity - in fact a local definition of a meter is the amount of distance light traverses in a certain amount of local time, so that as time warps, space also warps. This is usally much less significant as far as the motions of bodies go, but it does show up in such effects as the apparent deflection of light via a strong gravitational field as being twice that of what one would otherwise expect.
As far as falling into a black hole goes, if the hole is non-rotating, one is probably dead, not in an alternate universe.
There might be a small possibility of reaching a so-called alternate universe by falling into a rotating black hole rather than a rotating one, with enough planning. This is very much uncertain, though - it's not something I'd want to bet my life on. Since we won't ever be able to see the inner structure of a black hole without going beyond the event horizion, there is no way to determine experimentally the answer to this question, and it will remain beyond the confirmation of direct experiment.
For a discussion of some of the theoretical predictions of what MIGHT happen if one falls into a rotating black hole, I'd recommend Kip Thorne's book "Black holes and time warps: Einstein's outrageous legacy". Online there is a much more technical paper
http://lanl.arxiv.org/PS_cache/gr-qc/pdf/9902/9902008.pdf
that discusses this question.
I'm not aware if there are any papers that have superceeded this analysis, it is an analysis of the collapse of a charged scalar field as an indication of what MIGHT happen with a rotating black hole, it's not even a direct simulation of a rotating black hole!
But it does mention the possibility of reaching an alternate universe, for instance
Does the inner structure of a Reissner-Nordstr¨om black hole describe the generic outcome
of gravitational collapse? Novikov [5] studied the collapse of a charged shell and found that
the shell will reach a minimal radius and bounce back, emerging into another asymptotically
flat region - a different universe. The idea of reaching other universes via a black hole’s
interior is rather attractive. It immediately captured the imagination of the popular audience
and SciFi authors coined the “technical” term “Stargate” for this phenomenon. However as
predictability is lost at the CH this leads to serious conceptual problems.
We are faced with two gravitational collapse models. The “traumatic” collapse to
Schwarzschild in which nothing can escape the central singularity and the “fascinating”
collapse to Kerr or Reissner-Nordstr¨om in which a generic infalling observer might escape
unharmed to another Universe. Which of the two possibilities is the generic one?
Penrose, [6] who was the first to address this issue pointed out that small perturbations,
which are remnants of the gravitational collapse outside the collapsing object are infinitely
blueshifted as they propagate in the black-hole’s interior parallel to the Cauchy horizon.
The resulting infinite energy leads to a curvature singularity. Matzner et. al [7] have shown
2
that the CH is indeed unstable to linear perturbations. This indicates that the CH might be
singular - “Stargate” might be closed. A detailed modeling of this phenomena suggests that
the CH inside charged or spinning black-holes is transformed into a null, weak singularity
[8–10]. The CH singularity is weak in the sense that an infalling observer which hits this null
singularity experiences only a finite tidal deformation [10]. Nevertheless, curvature scalars
(namely, the Newman-Penrose Weyl scalar \Phi_2 ) diverge along the CH, a phenomena known
as mass-inflation [9].
I don't fully understand the nature of this "mass-inflation" singularity, but it appears that as the tidal forces are finite, it might be survivable. It's unclear whether or not this even means that a human could survive the resulting tidal forces, much less what the other effects of this so-called "weak" singularity are. It's not even totally clear that the actual singularity would be such a weak singularity, the language on this point is tentative.
All in all, going into a black hole would be an extremely risky proposition.
