gamma factor with negative m(r) function

This result is full of interest, and goes far beyond the standard model in which m(r) = 1 – r0 / r , a restriction imposed by the obsolete Einstein field equation. In order for m(r) < 1 in the standard model, the requirement MG > r c squared would be imposed. In the m(r) theory the possibility of an expanding orbit could be looked for in astronomy.

gamma factor with negative m(r) function

As can be seen from the graphics, the m function can be extended to
negative values without sacrificing the condition that the square root
in the generalized gamma factor retains positive arguments. For m(r)=0
it follos gamma=0 which leads to divergence in the equations of motion.
At this “event horizon” total energy and angular momentum are undefined.
For m(r)<0 the gamma factor first is in the superluminal regime but then
quickly rises to infinity. For these cases the equations of motion
should be solvable.
As can be seen from the classical limit of m theory (the equations I
sent over a couple of days before), in these equations the sign of m(r)
cancels out, these equations are insensitive to the sign. However the
gamma factor leads to a quite different behaviour for m>0 and m<0.
For 0<m<1 we found shrinking orbits. for m>1 the orbits should be
expanding. I will check this numerically.


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