I have pretty much wrote up all the details of my next paper I will submit and if you would like to see it just follow:

https://blackholeradiation.quora.com/

It covers related topics, of gravimagnetic and spin coupling, the quantization of the black hole for a true analogue theory of the ground state hydrogen atom. It covers why, if black hole particles can exist, they would need to obey Larmor radiation in the form of Hawking emission and I will argue why there are no stable black holes in nature from the equations I derived. I still need to write out conclusions, and sort footnotes and marking the references or even just sorting the references. The main equations are:

1. The gravimagnetic field for rotating systems is obtained from the master equation:

[math]\mathbf{B} = \frac{1}{mc^2 e} \frac{1}{r} \frac{\partial U}{\partial r} \mathbf{J} = \frac{1}{me}(\frac{\phi}{c^2})\frac{\partial v}{\partial t} \mathbf{J} = -\frac{1}{e}\frac{1}{Gm}\frac{\partial v}{\partial t} \mathbf{J}= -\frac{1}{me}\frac{a}{G} \mathbf{J} = -\frac{1}{me}\frac{\omega^2 r}{G} \mathbf{J} = -\frac{1}{m e} \frac{m}{r^2} \mathbf{J}[/math]

2. A spin density obtained from the master equation:

[math]e (\nabla \times \mathbf{B}) = -\frac{\mathbf{J}}{r^3} [/math]

3. The Von Klitzing factor appears invariant through many of the equations I looked at:

[math]e \mathbf{B} = \frac{ \mathbf{J}}{e^2 } \frac{\partial U}{\partial r}= \frac{1}{m}(\frac{\phi}{c^2})\frac{\partial v}{\partial t} \mathbf{J} = -\frac{1}{Gm}\frac{\partial v}{\partial t} \mathbf{J}= -\frac{1}{m}\frac{a}{G} \mathbf{J} = -\frac{1}{m}\frac{\omega^2 r}{G} \mathbf{J} = -\frac{1}{m} \frac{m}{r^2} \mathbf{J}[/math]

4. Angular precession of a particle due to torsion is

[math]\omega = -\frac{\Omega}{2} = \frac{e \mathbf{B}}{2m} = \frac{\mathbf{J}}{2e^2} \frac{1}{m}\frac{\partial U}{\partial r} = \frac{1}{2m^2}(\frac{\phi}{c^2})\frac{\partial v}{\partial t} \mathbf{J} = -\frac{1}{Gm^2}\frac{\partial v}{\partial t} \mathbf{J}= -\frac{1}{2m^2}\frac{a}{G} \mathbf{J} = -\frac{1}{2m^2}\frac{\omega^2 r}{G} \mathbf{J} = -\frac{1}{2m^2} \frac{m}{r^2} \mathbf{J}[/math]

5. Curl of the torsion field is:

[math]\nabla \times \Omega = \gamma \frac{\partial \mathbf{B}}{\partial r} = \frac{e}{2m} \frac{\partial \mathbf{B}}{\partial r} = \frac{\mathbf{J}}{2e^2} \frac{1}{mc^2}\frac{\partial^2 U}{\partial t^2} [/math]

6. Velocity coupling to gravimagnetic field is shown with coupling constants (gravitational fine structure):

[math]\mathbf{B} \times v = \frac{\alpha_G}{e} \frac{\partial U}{\partial r} = \alpha_G \frac{\partial \mathbf{V}}{\partial r} = \frac{m}{ e}\frac{G}{2c}\frac{\mathbf{J} - 3(\mathbf{J} \cdot \frac{\mathbf{r}}{r}) \frac{\mathbf{r}}{r}}{r^3}[/math]

7. It's also true as:

[math]\Omega \times v = \gamma (\mathbf{B} \times v) = \frac{G}{2c}\frac{\mathbf{J} - 3(\mathbf{J} \cdot \frac{\mathbf{r}}{r}) \frac{\mathbf{r}}{r}}{r^3}[/math]

8. A Hamiltonian spin-orbit coupling equation is presented as:

[math]H = \frac{1}{2}\Omega \cdot \mathbf{L} = \frac{e \mathbf{B} \hbar}{2m} = \frac{\mathbf{J} \cdot \mathbf{S}}{2e^2} \frac{1}{m}\frac{\partial U}{\partial r} = \frac{1}{2m^2}(\frac{\phi}{c^2})\frac{\partial v}{\partial t} \mathbf{J} \cdot \mathbf{S} [/math]

[math] = -\frac{1}{Gm^2}\frac{\partial v}{\partial t} \mathbf{J} \cdot \mathbf{S} = -\frac{1}{2m^2}\frac{a}{G} \mathbf{J} \cdot \mathbf{S} = -\frac{1}{2m^2}\frac{\omega^2 r}{G} \mathbf{J} \cdot \mathbf{S} = -\frac{1}{2m^2} \frac{m}{r^2} \mathbf{J} \cdot \mathbf{S}[/math]

9. The traditional definition for the torsion field finds one such term from the master equation:

[math]\mathbf{B} = \frac{1}{mc^2 e} \frac{1}{r} \frac{\partial U}{\partial r} \mathbf{J}= \frac{m}{ e} \frac{1}{mc^2} \frac{\partial U}{\partial t} = \frac{m}{ e}\frac{G}{2c^2}\frac{\mathbf{J} - 3(\mathbf{J} \cdot \frac{\mathbf{r}}{r}) \frac{\mathbf{r}}{r}}{r^3}[/math]

10. Related to the previous gravimagnetic field, an equivalent form:

[math]\gamma \mathbf{B} = \frac{e\mathbf{B}}{2m} = \frac{1}{m^2c^2} \frac{1}{r} \frac{\partial U}{\partial r} \mathbf{J}= \frac{1}{mc^2} \frac{\partial U}{\partial t} = \frac{G}{2c^2}\frac{\mathbf{J} - 3(\mathbf{J} \cdot \frac{\mathbf{r}}{r}) \frac{\mathbf{r}}{r}}{r^3}[/math]

11. Field strength is found as

[math]\mathbf{H} = \Omega \times v = \frac{G}{2c}\frac{\mathbf{J} - 3(\mathbf{J} \cdot \frac{\mathbf{r}}{r}) \frac{\mathbf{r}}{r}}{r^3}[/math]

12. With an equivalent formula:

[math]\mathbf{H} = \gamma (\mathbf{B} \times v) = \frac{e(\mathbf{B} \times v)}{2m} = \frac{G}{2c}\frac{\mathbf{J} - 3(\mathbf{J} \cdot \frac{\mathbf{r}}{r}) \frac{\mathbf{r}}{r}}{r^3}[/math]

13. The gravimagnetic force is directed, just like a Lorentz force which is perpendicular to both the velocity and the strength of the gravitomagnetic field ~

[math]\mathbf{F} = \frac{m}{c}(v \times \mathbf{H}) = \frac{Gm}{2c}\frac{\mathbf{J} - 3(\mathbf{J} \cdot \frac{\mathbf{r}}{r}) \frac{\mathbf{r}}{r}}{r^3}[/math]

14. Sciama's theory can be implemented on the field strength as a cross product:

[math] \mathbf{H} \times (\frac{\phi}{c^2}) = \frac{m}{r^2} = \frac{1}{2c}\frac{\mathbf{J} - 3(\mathbf{J} \cdot \frac{\mathbf{r}}{r}) \frac{\mathbf{r}}{r}}{r^3} \approx \mathbf{E}[/math]

15. There is a scalar triple product::

[math]\nabla \cdot (\mathbf{H} \times (\frac{\phi}{c^2})) = (\frac{\phi}{c^2}) \cdot (\nabla \times \mathbf{H}) = \frac{m}{r^3} = \frac{1}{2c}\frac{\mathbf{J} - 3(\mathbf{J} \cdot \frac{\mathbf{r}}{r}) \frac{\mathbf{r}}{r}}{r^4} \approx \nabla \cdot \mathbf{E} = 4 \pi \rho[/math]

16. The pseudo-quantization of the field is:

[math]n \hbar = e\oint_S\ \mathbf{B} \cdot dS = \frac{\mathbf{J}}{e^2} \int \int_S\ \frac{\partial U}{\partial r} \cdot dS[/math]

**Edited by Dubbelosix, 20 October 2018 - 12:36 PM.**