In "snow globe theory", a potential can be defined. It describes the relative change in the speed of light at great distances.
The value is calculated from the change in length scale/change in time scale, i.e., P=1/(1+T/R)².
With Q=G•M, T=Q/c² is half the Schwarzschild radius (rs).
The table shows the comparison in the solar system (T=1476 m) with the Schwarzschild potential 1-rs/R.
The red/blue shift at great distances with "snow globe theory" and the Newtonian potential E*-Q/R is calculated as N=T/R.
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This potential can also be used in the Schwarzschild metric.
Unlike the Schwarzschild potential, it has no singularity for R other than 0.
However, it uses the Newtonian potential E-Q/R, which may only be asymptotically correct (for weak forces or large radii).**
Otherwise, the event horizon (according to my definition) would always be at G•M/c² with local light speed and Newtonian gravity.
Derivation:
According to my definition, the event horizon would be the radius at which light is bent in a circle.
s=V0•t+(a/2)•t² s is the distance, V0 initial velocity = 0, a constant acceleration, t time.
The second derivative, say (here, the light path) curvature, of a parabola with equidistant h and radius of curvature rk is calculated as follows:
1/rk=(sleft+ sright-2•scenter)/h²
With a = Newtonian gravity = G•M/R², sleft= sright=0, the light path h=c•t results in t -> 0:
R=rk=-G•M/c² for a circular light deflection. The negative sign comes from this:
The acceleration is directed upward, the curvature downward.
Why upward? The (apparent) force is opposite to the acceleration.
When I accelerate on my bicycle, inertia pushes me backward.
Note:
If a light beam travels perpendicularly from a stationary path, it is straight. From a moving object along the path,
it appears slanted, and from an accelerating system, it appears curved.
The Einstein elevator describes this for gravitational acceleration.
*Maximum potential energy, usually set to zero.
**The solution
Ludwig Resch
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