Nice question.
If General Relativity were exactly true at all scales, then somebody falling in to a black hole would hit a singularity. However, your speculation that something changes on a small scale is very much the standard view now. The existence of any sort of classical field makes extreme logical difficulties for quantum mechanics. Therefore it's generally assumed that the full theory of gravity will be quantized, with GR emerging as the large-scale limit. On the scale of quantum gravity (the Planck scale, ~ 10
-33cm) something else takes over, replacing the approach to the singularity. String theory is the most popular current approach to that problem.
Mike W.
unchecked post, Lee's in Paris.
(published on 11/30/2011)
