I won’t say I am calm but I see an error. The characteristic Schwarzschild radius of E4 meters is E-12 light-years. Thus the result is a factor of 10 smaller. The expansion indicated here equals the original geometric ‘R’ of the universe.
Given the wide-angle sort of pic I hosted a few days ago of galaxies arrayed like tops, or stones, could we believe there are on the order of one trillion of them ??? This is a rough answer, given the Milky Way spreading about E5 lightyears. I take ten times this distance, which may be too small, to the next galaxy.
Steve sends a 2011 paper by Kim Greist, with the correct integration for proper distance. The result is used only for near-field study. Very soon my brother and I will issue some VERY LARGE NUMBERS, of all the black holes ‘around’.
Given a little time backed away from this, I see now we invert the limits of integration, but changing the ± is not the same. Thus the two distinct forms, for proper distance.
I need my faithful factotem, Pitro Rumenov Todorov, a Bulgarian student in Wisconsin, who once intoned, “The mantissa is the decimal part of the expression of a logarithm.”