Quote:
Originally Posted by czeslaw
What is a diameter of the Naked Singularity ?
Is it like a Black Hole diameter ?
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The diameter is the diameter of the magnified heterotic superstring class 1 of the Planck-Lengthx2.
This is known as heterotic superstring class 8x8, where the Planck-Length has increased to 10^-22 metres.
The naked singularity is of dimension 0, implying that there is a curvature embodied in the so called Kerr-Torus.
The Kerr-Torus has a 'little' radius of the Planck-Length (Sqrt(hG/2Pi.c^3)) and a 'big' radius of 10^-22 metres.
The 0D can be constructed in the following way.
Imagine the Kerr-Torus to NOT have any 'hole' in the middle.
Then draw a circle of radius R and halve R to inscribe two smaller circles into the bigger one (of diameter 2R). Apply solid-of-revolution 'calculus' say to project the circles into 3D (to visualise).
The circle's centre now exhibits the two curvatures (negative and positive) simultaneously if one delocalises or doubles the observer frames.
Placed at the centre, the curvature is hyperbolic for an open universe and any point outside the big circle will show the curvature as closed (one simply looks at the sphere).
Now there are exactly 8 smaller sphere volumes 4Pi(R/2)^3 inside the big sphere of 4PiR^3/3.
But the geometrical construction also defines a Torus Volume Pi.r^2x2Pi.r=2Pi.r^3 as the lineintegral of the smaller circle around the enclosing sphere.
{Note that the construction above eliminates the hole in defining the inside 2D smaller circles as touching each other.
If there is a gap, then the lineintegral of 2PiR will NOT be 2Pir as in the above, but R>r.}
This differs in the ratio 3Pi/2=4.712... and as the upper bound for the Chaos Constant (or Feigenbaum delta 4.66..) and is simply the ratio of aTorus of radius R=r to the bigger sphere in 2Pi^2.R^3=(3Pi/2)x(4Pi.R^3/3).
As the lineintegral can be said to be 1-dimensional as the extension of a point; the curvature or curling of this 1st dimension about itself becomes the 0th dimension.
And this is just the definition of the Planck-Boson as class 1, having both openended and closed superstrings as vibration patterns; all other classes being exclusively closed.
Tony B.