Dr. Vivian Robinson comment for whoever remembers math - culprit was in 1/(1+ε) ≠ 1-ε :

Dr. Vivian Robinson: “I have a printed and updated version in an Institute of Physics (UK) Journal. You can view it at:

https://doi.org/10.1088/2399-6528/abee2f

It is worth pointing out that Einstein derived the term 1/(1+alpha/r). He approximated it to (1 — alpha/r). Within the solar system, that is a valid approximation when alpha/r is less than 10^–6 and experimental accuracy is less than 1 in 1000. When Schwarzschild derived his metric, he continued that approximation as he derived the term (1 — alpha/R), where R = cube root [(r³ + alpha³)]. When r = 0, R = alpha, so (1 — alpha/R) only goes to zero at r = 0. The inverse, 1/(1 — alpha/R) only goes to infinity at r = 0. If you look at equation (29) in my above referenced paper, which is an exact solution to Einstein’s field equations, you will find it also gives an infinity at r = 0. For r >> alpha, as applies in our solar system, Schwarzschild’s solutions give the same result as obtained from Einstein’s calculations. There was no need for Einstein to find fault in the mathematics.

Those who followed Schwarzschild replaced R with r. There was no justification in mathematics or physics for that change. It was that move that gave rise to 1/(1 — alpha/r) term that predicts the singularity at r = alpha. That is a simple mathematical error for which there is no justification. It makes me wonder if any of the cosmologists who rave on about black holes ever read either Schwarzschild’s solution or Einstein’s derivations of his field equations. Singularities at r = alpha can’t be derived from either Einstein’s field equations or Schwarzschild’s solution.”