PS : I think that the small difference could be due to the fact that the potential energy in the (r, phi) and (r1, phi) coordinates systems are different, i. e -mMG / r in (r, phi) and -mMG / r1 in (r1, phi). You have demonstrated numerically that this difference does not affect the conservation of H and L, and you have also shown that conservation is a very rigorous condition of self consistency of both the analytical and numerical methods. By definition r1 = r / sqrt m(r), so at the event horizon in the obsolete Schwarzschild metric, m(r) (= 1 – r0 / r) goes to zero at the event horizon, r = r0, and so r1 approaches infinity and the potential energy in (r1, phi) approaches zero. However in (r, phi) the potential energy remains finite at the event horizon. This shows the great importance of doing everything in frame (r1, phi). In fact the new cosmology of UFT416 gets rid of the Schwarzschild singularities, and gets rid of the incorrect Einstein equation.

Preliminary version of UFT 416,3

Many thanks, and full of interest. I will update and correct Eqs. (42) and (43) so that they are precisely the same as in your Section 3, then repost Sections 1 and 2. I think that there are a couple of typographical errors in the preliminary version of Section 3 as follows.

1) In Eq. (60), replace r dot by r1 dot and r by r1.

2) The figures cannot be seen in this version, but will appear in the final version.

3) In the final three figure captions it should be “Schwarzschild”.

The completed and reposted UFT416 will introduce an entirely new and rigorously self consistent cosmology. Preliminary version of UFT 416,3

To: Myron Evans <myronevans123>

In Eqs. (42,43) seem to be some typos, but anyway, I have repeated them in section 3. The equations of motion for the (r_1,phi) coordinate system I have derived from the Lagrangian (33). The equations are simpler as expected, since m(r_1) now appears only once in the Lagrangian. I had expected that in the numerical results the same results came out as for the (r,phi) coordinates where r has been transformed to r_1 a posteriori. However there seems to be a slight difference. I am not sure for the reason. In the (r_1,phi) coordinate system there is no r coordinate, therefore the m function has to be taken with r_1 as an argument, where it was r in the observer system. This could be the reason. Have you an idea if this could make a difference?

Horst

Am 11.10.2018 um 11:25 schrieb Myron Evans:

FOR POSTING: UFT416 Sections 1 and 2 and Background Notes

This is UFT416 which introduces a rigorously self consistent and powerful new cosmology able to describe any observable orbit. Horst’s Section 3 is ready to be added and contains many important new results. It would be important to write Eqs. (42) and (43) in the correct (r1, phi) coordinate system in Section 3. These sections give a triple cross check of quantities such as the conserved angular momentum. This is also demonstrated numerically by Horst, giving a quadruple cross check.