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.

*Comments*

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.

DETAILS: I have asked this to Steve Albers !!!!! IT says every BH adds a bit of size to the universe ??? At a light year, that’s 3 E8, 365 x 24 x 3600 meters, let’s see. Logarithms are to base ‘e’, so a factor of 10 is roughly 2.5 in base ‘e’. Thus a light-yea…

What’s the log of 10 billion light-years ?? Let’s scale to the 100 km. so if the Universe is E26 m, then it is E21 times our scale. THE EXPRESSION HAS A SQUARE ROOT, so call it E10.5, and a factor of 2 so call it E11. Log of this is about 33.

THIS SEZ ONE BLACK HOLE adds to the Universe quite a bit of total volume !!! What exactly do I mean?? There is extra radius IN THE FAR, and it can amount to 3 E6 meters. Given that there exists a certain small but regular density of black holes per cubic parsec or some large volume of space..

>>> I pick up another factor of 30, since the value of the √r from inside the first term’s square root, becomes larger than the log, and at one million, this is the factor. SO EACH BH ADDDS E8 meters to the UNIVERSE. That’s a ‘chunk of change”.

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