Aharon Davidson, Ben Yellin
Generalizing Dirac's procedure to time dependent systems, we derive a reduced total Hamiltonian, resembling an upside down harmonic oscillator, which generates the Schwarzschild solution in the mini superspace. Associated with the circumferential radius dependent Schrodinger equation is a tower of localized Guth-Pi-Barton wave packets, orthonormal and non-singular, admitting equally spaced average-'energy' levels. The Schwarzschild vacuum, corresponding to a vanishing mean mass, is accompanied by a detailed mass uncertainty spectrum. The latter is proven to be universal, accompanying the massive Schwarzschild sector for any arbitrary mean mass. The horizon surface area exhibits a linear spectrum, treating mean masses and mass fluctuations on equal footing.
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http://arxiv.org/abs/1208.6261
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