Monday, April 24, 2017

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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