Warren, Problems I see with equasions as you presented them.

There is no Accounting of Gravity, Distance, and atom motions all of which are likely to prevent atoms from even impacting or getting close the the black hole. Your equasions seem to assume that all matter that is close will be pulled in and absorbed. That isn't the case at the atomic/quantum level.

There is no Accounting for Objects in the process of being captured, from preventing other objects from getting close. Atom1, in a death spiral into BH, still has electron shell, which deflects atom 2 away from itself and the BH.

Overall the equasions need to be reworked to account for the Probability of atom-atom collisions based on temperature first, (modified to remove the electron shell repulsion of normal matter)

Once you have the probibility of collision (Pc) at temp t, over time T, then you can work this into your existing equasions. However you'll likely get a result more in line with billions or trillions of years, unless the BH mass starts out as a few kg's.

This is what I meant before about accouting for quantum interactions. Those are all probibility based, and the person writing that paper is totaly ignoring them.

Which you can't. If something is as small, (or Smaller) then an atom, then quantum rules always apply. Even to Black Holes. Which means the absorbsion rates will be based on the result of probibility of a collision over some time first.

Not to mention a whole slew of motion, charge, and other force interactions not accounted for in his paper.

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