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We study the end stages of gravitational collapse of the thin shell of matterin ingoing Eddington-Finkelstein coordinates. We use the functional Schrodingerformalism to capture quantum effects in the near singularity limit. We findthat that the equations of motion which govern the behavior of the collapsingshell near the classical singularity become strongly non-local. This reinforcesprevious arguments that quantum gravity in the strong field regime might benon-local. We managed to solve the non-local equation of motion for the dustshell case, and found an explicit form of the wavefunction describing thecollapsing shell. This wavefunction and the corresponding probability densityare non-singular at the origin, thus indicating that quantization should beable to rid gravity of singularities, just as it was the case with the singularCoulomb potential.

Non-local (but also non-singular) physics at the last stages of gravitational collapse