15. Maximum velocity in pure gravitational field

According to Lorentz effect in the gravitational field, 

 

(1)  $2GM_N/r_Nc^2=2f(N)=\pi((N-1)!+1)/N$

 

(=$N\pi$ when they are scattered)

 

In pure gravitational field, there is the relation like this, $GM/rc^2=1/\beta$. From (1),

 

$\beta=rc^2/GM \approx 2N/\pi((N-1)!+1) \leq 2/\pi$, $(N=2)$

 

This is because there is a minimum length $r_h$ and when external conditions are same, mass (or density) is not directly proportional to diameter. Even if $N$ is $1$, whether you set the value $0!$ to $0$ or $1$, the result is the same. Rather, the speed of light is reached when combined with wave energy. However, it may be different if we consider cases where time or space is discontinuous.

 

Previously, it was mentioned about 'non-smooth but differentiable functions'. The advantage of these functions is that they make it easier to integrate, differentiate, calcuate functions with others, even if they cannot be seen in the actual physical world. If the gamma function $\Gamma$ is introduced here, it becomes as follows, and the above minimum value may vary depending on the $z$ value.

 

$\beta=2z/\pi(\Gamma(z)+1)$