Ed ~ the obvious solution is that r is never equal to 0. The smallest point of spacetime is 10^-42, and Heisenberg uncertainty principle dictates that this singularity is smeared over a finite area. However an understanding of the physics still requires a new theory of quantum gravity to be formulated.
Leading physicists attempt to answer the question: "What are black holes made of?" Those questioned include Professors Andrew Strominger, Michio Kaku, Lawrence Krauss, Max Tegmark, Ramesh Narayan and Douglas Leonard.
Horizon: Who is afraid of a big black hole was on BBC Two at 21:00 BST on Tuesday 3 November. Watch repeat with BBC iPlayer.