Modelling quantum black hole
  Novel bound states are obtained for manifolds with singular potentials. These singular potentials require proper boundary conditions across boundaries. The number of bound states match nicely with what we would expect for black holes. Also they serve to model membrane mechanism for the black hole horizons in simpler contexts. The singular potentials can also mimic expanding boundaries elegantly, there by obtaining appropriately tuned radiation rates. 
T. R. Govindarajan and J.M. Mun\~oz-Casta\~neda
hep-th gr-qc math-ph math.MP quant-ph