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• Chart Of Mass Infall From Infinity: Relativistic And Newtonian Mass Velocity And Energy Ratios
• Table Of Relativistic Data Computations For Above Chart
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### CHART: Relativistic Mass, Velocity, And Energy Ratios Mass Fall From Infinity Toward A Singularity

The above chart depicts relativistic increase in Mass as Speed asymptotes to the speed of light 'c'. The example chosen is for a 1 Slug mass falling from infinity into a 10SM Black Hole. Position along the horizontal axis is made dimensionless [normalized] by dividing the infall position distance by the Schwarzschild radius. The chart result is therefore correct for Black Holes of any mass. The chart grid is shaded darker to the left of Position/Rs=1 [Event Horizon]; the dark area represents the interior of the Black Hole with the singularity located at 0.0 at left side of chart.

Notice the green trace of Energy ratio versus position; Since kinetc energy from gravity Work done is found from W=GM/R the energy trace is linear as seen on a log-log plot. There are no 'relativistic effects' on accumulated energy. The blue trace shows infall velocity of the mass approaching 'c' [asymptote] as position drops below about 4Rs. A black dotted line centered on blue (right side of chart) shows Newtonian velocity. This velocity= 'c' at Position=Rs=1 which is the current definition of the Schwarzschild 'event horizon'; I like to assign the term "Schwarzschild Energy" to that energy attained for Position=Rs (for a mass dropped from infinity).

The red trace shows the relative increase in mass as the body becomes relativistic. The black horizontal dotted line in the middle of the red trace on the right represents the Newtonian mass; and is is always equal to one since Newtonian mass is constant independent of velocity.

So what the chart shows is that as speed asymptotes to 'c', the constantly accumulating energy becomes manifest in relativistic mass increase; this increase in mass ratio is is called 'Gamma' and is found from Einsteins contraction 1/sqrt(1-(v/c)^2)^.5.

Notice also that the {Newtonian velocity] dotted line aligned with blue intersects the 0.01 distance (on left) at 10.0. The Newtonian velocity at this position would be 10x the speed of light and with mass=1 the energy would be 100. This jives with the relativistic energy result where Vr~=c and Mr is ~100x times rest mass making the energy the same 100.

Another very interesting find is that the mass increase 'Gamma' is identical to the Fibonacci Ratio when Position= Rs. I believe this result is correct; The result falls out of the solution of the equations for gravity Work W=GM/R set equal to Energy E=M(V^2)/2 after correcting for relativistic mass increase. Energy E=(M)(Vr^2)/(1-(Vr/c)^2)^(.5). This equation can be solved as a quadratic. TBD, I will post the math in a MS paint cartoon.

### TABLE: Computational Spread Sheet Results For The Chart

Notice 'Gamma' (highlighted red) showing the Fibonacci number when the mass has fallen to the event horizon at the Schwarzschild radius distance from the singularity! I am attempting to run numbers to get comfortable or not with accelerating expansion of the universe. I am likely less qualified than those doing the investigation, but the concept is troubling to me. I am trying to determine if maybe the Hubble constant is modified by relativistic contraction; and wondering if such a mod would change the expansion conclusion back to 'decelerating'.