Avoidance of Classical Singularities in Quantized Gravitational Dust Systems

Abstract

We use the canonical quantization of spherically symetric dust universes, and calculate the expectation value of the quantized metric, $<Ψ|\hat{g}|Ψ>$. Though the classical solutions are singular, and the wave functions have no zero support on singular geometries, the expectation values are everywhere regular. For a quasi-classical (coherent) state, the metric expectation value describes a universe (or star) that collapses to a minimum radius, the Planck radius, and re-expands again.