Black holes and quantum theory on manifolds with singular potentials
  Quantum theory on manifolds with boundaries have been studied extensively through von Neumann analysis of self adjoint operators. We approach the issues through introduction of singular $\delta$ and $\delta'$ potentials. The advantages of this are pointed out as a model for black hole and in several other examples. 
T R Govindarajan and J. M. Munoz-Castaneda
math-ph gr-qc hep-th math.MP quant-ph