I think I am smart, and I think Stephen Wolfram is a genius. He gives me an analytic statement for my exterior integral, which had me stumped. My statement about needing extra ‘rope’ stands, and in fact the plot gets even a little better !!! We will need at least an amount at least equal to the BH size, the Schwarzschild radius. Observe: ∫ √r/(r-1) dr is given as: √r(r-1) + log [ √r + √(r-1) ] . YAAAAAAAY. In the very far, even ‘r’ gets much larger than its logarithm. The square of ‘r’ trumps, but there are small ‘leftovers’ !!!
The residue terms are analyzable, and start at zero, slowly increasing. The conclusion is there is at least ‘2m’ of “extra distance” outside, and indeed this figure keeps climbing slowly. That’s spooked. Sure compared with the value of some large ‘r’, the square is arbitrarily larger than it, and also compared with the log (2r) . ARE THERE ANY IMPLICATIONS ON A COSMIC SCALE ???? I ran some numbers over on FaceBook.
Now the next morning, I see the term from square root of radius becomes larger than the log term, so I guess each BH adds E8 meters to the UNIVERSE RADIUS.