Schwarzschild Mass Uncertainty
  Applying Dirac's procedure to $r$-dependent constrained systems, we derive a reduced total Hamiltonian, resembling an upside down harmonic oscillator, which generates the Schwarzschild solution in the mini super-spacetime. Associated with the now $r$-dependent Schrodinger equation is a tower of localized Guth-Pi-Barton wave packets, orthonormal and non-singular, admitting equally spaced average-'energy' levels. Our approach is characterized by a universal quantum mechanical uncertainty structure which enters the game already at the flat spacetime level, and accompanies the massive Schwarzschild sector for any arbitrary mean mass. The average black hole horizon surface area is linearly quantized. 
Aharon Davidson and Ben Yellin
gr-qc