Earlier, back around 2001, Martin Bojowald got rid of the Big Bang singularity and since then many authors have repeated this using quantum gravity methods, their results confirming Bojowald's: there was no singularity, it goes away when the classical equations are quantized. Classical Gen Rel had two famous singularities: the Big Bang and the Black Hole. the first of these seems to have been cured by the work subsequent to the 2001 paper. Now it looks like Bojowald is preparing to look at the second, the black hole singularity. he and another person at Albert Einstein Institute (MPI Potsdam) have diagonalized the volume operator in the spherically symmetric case and gotten the volume spectrum it looks like energy levels of an atom the homogeneous/isotropic case volume spectrum was calculated some years back and this what they show now looks like "line splitting" it refines the homogeneous/isotropic case gravity is geometry so the quantities you measure, instead of being quantities like energy, can be geometric quantities like curvature and area and volume so not so unlike Bohr studying the energy spectrum of the hydrogen atom a century ago, Bojo and co-worker have to study the volume spectrum of a black hole---it is their atom and the spectrum looks sort of nice, I will get a page reference for it. I dont get any feeling that they are near to removing the singularity, just that they are setting up to consider it----doing ground work to get ready to look at LQG black holes http://arxiv.org/abs/gr-qc/0407018 "The Volume Operator in Spherically Symmetric Quantum Geometry"