## Complete m theory for shrinkng orbits – part 3

This is full of interest and this message acknowledges receipt. I will study the results in detail and comment tomorrow, pressing on with sections 1 and 2.

Complete m theory for shrinking orbits – part 3

I investigated the effect of separating two spherical regions by a surface m(r_0)=0. Here r_0 is something like an event horizon.
F21: m(r) for r_0>0.3. The negative part is not relevant.
F22: example of periodic orbit for outside the horizon. There is an alternating elliptical motion of near and and wide distances to the horizon.
F23: example of collapsing orbit for outside the horizon. The r coordinate ends at the horizon while r_1 is repelled. Whether this repelling occurs, depends on details of m(r) and probably initial conditions.
F24: m(r) for r_0<0.3 (inner part of horizon)
F25: periodic orbit within horizon. This is not different from outer motion, except that r and r_1 differ near to the horizon, not near to the centre.
F26: collapsing orbit within the horizon. After one round the orbit expands and the mass moves to the horizon. For the r coordinate this is the end point while r_1 goes beyond the horizon.

Comparing the behaviour with the event horizon of EGR, there is a coordinate boundary of the Lagrange coordinate r at the horizon. However there is no singularity of the coordinate. However an anomalous behaviour could appear for the oberserver coordinate r_1, which can pass through the horizon. This is similar to alleged black holes where matter can pass the event horizon which is mainly a coordinate singularity. However the standard modelers do not make a difference between the r parameter and a real radius coordinate. r is a curvature parameter as Stephen Crothers has pointed out.

I think this is enough material for section 3 of UFT 416, except some special questions that could arise during discussion additionally.

Horst

Am 07.10.2018 um 20:46 schrieb Horst Eckardt:

This is the same calculation as before with the exponential m function .
F11: orbits r(phi) and r1(phi). Parameters are a bit more less deviating from m=1 than in the case I sent over before. The r1 orbit is slightly larger than the r orbit as before but both go to zero for m–>0. This may either be an effect of the curve form of m(r) or because the exponential m function behaves less exotic.
F12: The behaviour of the orbits is demonstrated by the trajectories r(t) and r1(t). Both converge.
F13: Velocities v, v1, corresponding to r, r1. Both velocities go to zero for r–>0, m–>0.

Horst