QGD prediction of the Density and Size of Black Holes

QGD predicts that black holes are extremely dense but not infinitely so. Considering that $preon{{s}^{\left( + \right)}}$ are strictly kinetic and that no two can simultaneously occupy any given $preon{{s}^{\left( - \right)}}$ then $\max densit{{y}_{BH}}=\frac{1preo{{n}^{\left( + \right)}}}{2preon{{s}^{\left( - \right)}}}or\frac{1}{2}$ . It follows that $\min Vo{{l}_{BH}}=2{{m}_{BH}}preon{{s}^{\left( - \right)}}$ or, since $preo{{n}^{\left( - \right)}}$ is the fundamental unit of space, we can simply write $\min Vo{{l}_{BH}}=2{{m}_{BH}}$ for the minimum corresponding radius $\min {{r}_{BH}}=\left\lfloor \sqrt[3]{\frac{3{{m}_{BH}}}{2\pi }} \right\rfloor$ .

For the radius of the black hole predicted to be a the center of our galaxy, ${{m}_{BH}}\approx 4*{{10}^{6}}{{M}_{\odot }}$ and $\min {{r}_{BH}}=\left\lfloor \sqrt[3]{\frac{3{{m}_{BH}}}{2\pi }} \right\rfloor \approx 1.24*{{10}^{2}}{{M}_{\odot }}$ where the mass is expressed in $preon{{s}^{\left( + \right)}}$ and radius in $preon{{s}^{\left( - \right)}}$ . Though converting this into conventional units requires observations to determine the values of the QGD constants $k$ and $c$ , using relation between QGD and Newtonian gravity, we also predict that the radius within which light cannot escape a massive structure is $\displaystyle {{r}_{qgd}}=\sqrt{{{G}_{const}}\frac{M}{c}}$ where $\displaystyle {{G}_{const}}$ is used to represent the gravitational constant. Since the Schwarzschild radius for a black hole of mass ${{M}_{BH}}$ is ${{r}_{s}}={{G}_{const}}\frac{{{M}_{BH}}}{{{c}^{2}}}$ then $\displaystyle {{r}_{qgd}}=\sqrt{c{{r}_{s}}}$ .

Using ${{r}_{qgd}}$ to calculate ${{\delta }_{{{r}_{qgd}}}}$ the angular radius of the shadow of Sagitarius A*, the black hole at the center of our galaxy, we get ${{\delta }_{{{r}_{qgd}}}}\approx 26.64*{{10}^{-5}}$ arcsecond as a minimum value which is about 10 times the angular radius calculated using the Schwarzschild radius which i ${{\delta }_{{{r}_{s}}}}=27.6*{{10}^{-6}}$ arcsecond. This prediction will be tested in the near future by the upcoming observations by the Event Horizon Telescope.

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