Planck Philosophy...
JesseM said:
Is this equation something you derived yourself based on your own ideas, or did you get it from a textbook or something written by a professional physicist?
\boxed{\rho_u = \frac{M_u}{2} \sqrt{ \frac{c^3}{\hbar G}}}
The solution for this 'non-rotating' classical schwarzschild singularity density for a one dimensional 'point-like' object was derived by me based on research on these physical models.
Note that the Schwarzschild solution is only a solution for Schwarzschild BHs with zero angular momentum , this is a highly improbable state.
Neutron star spin increases with increased density, therefore an object generating in the core of a neutron star or supernova without spin is...impossible. Only BHs with angular momentum can exist in the Universe, a rotating Kerr BH.
JesseM said:
Would you agree that according to classical GR alone, the singularity has infinite density?
The Classical General Relativity model is based upon four total dimensional space-time n_t = 3 + 1 = 4 (3 space + 1 time). Solutions for models for that contain dimensions of less than four are not valid solutions in the Universe.
The classical solution stated for 1 dimension is actually 2 dimensions n_t = 1 + 1 = 2 (1 space + 1 time), because solutions with with a total dimensional range of less than 4 n_t < 4 cannot exist in the Universe, all solutions for total dimensional ranges between 0 and 3 are not real valid solutions because they cannot exist in a four total dimensional General Relativity Universe.
Classical General Relativity models based upon 0 to less than 2 total dimensions are typical of producing solutions with 'infinities', and is only a division by zero in an 'undefined' model.
This solution is based upon 2 dimensional space, the singularity described 'exists' in only 2 space dimensions (and 1 time) n_t = 2 + 1 = 2 (2 space + 1 time). n_t = n_s + n_t.
Classical Schwarzschild Singularity Dimension Number:
n_s = 2 - dimension #
dV_s = \pi r_p^2 - volume
L = 0 - angular momentum
Solution for 'non-rotating' Classical Schwarzschild Singularity Density for a two dimensional 'point-like' object: (flat disc)
\rho_s = \frac{dM_s}{dV_s} = \frac{dM_s}{\pi r_p^2} = \frac{M_u c^3}{\pi \hbar G}
\boxed{\rho_u = \frac{M_u c^3}{\pi \hbar G}}
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Chronos said:
I would argue the Planck density is the limit in the physical universe.
In a four dimensional space-time physical Universe, the average Planck density is a solution and a physical 'limit' in the Universe.
Based upon the current logarithmic slope in the chart, at what density value does the slope cross the y-intercept?
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Reference:
https://www.physicsforums.com/showpost.php?p=370142&postcount=24
