Nonlocal (but also nonsingular) physics at the last stages of gravitational collapse

We study the end stages of gravitational collapse of the thin shell of matter in ingoing Eddington-Finkelstein coordinates. We use the functional Schrodinger formalism to capture quantum effects in the near singularity limit. We find that the equations of motion which govern the behavior of the collapsing shell near the classical singularity become strongly nonlocal. This reinforces previous arguments that quantum gravity in the strong field regime might be nonlocal. We managed to solve the nonlocal equation of motion for the dust shell case, and found an explicit form of the wave function describing the collapsing shell. This wave function and the corresponding probability density are nonsingular at the origin, thus indicating that quantization should be able to rid gravity of singularities, just as was the case with the singular Coulomb potential.