Is there a singular point at the center of a black hole?

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In previous question “Can a black hole exist?”, simulation results of a gravity contracting dust ball was explained. Here, I explain the simulation results a little more.

!! CAUTION !! This is “MY QUESTION”. This can be in discord with standard view.

Time dilation is stronger where the gravity potential is lower. Thus, the effect is stronger near the center of the dust ball than outer region. In Newtonian dynamics, if a stationary spherically symmetric dust ball begin to fall at the same time, all dust reaches at the center point simultaneously. But if the time dilation is stronger in the center region like this case, dust at the outer region falls faster while dust at inner region has not gained due speed. Consequently, mass of the dust ball is concentrated on the outer shell.

When the concentrated shell falls further and it nears the Schwarzschild radius, time dilation increases steeply and proper time almost stop proceeding. Observed from us far from it, dust seems to stop falling and floating in the air. This must be the final state of the dust ball observed from us.

Even in this final stage, falling process of the central region has not proceeded enough and the density keeps thinner than outer region.  As a result, with the scenario that a black hole is formed from contracted dust ball, any thicker region, needless to say singular point, do not seem to appear at all.

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