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To be honest, we were somewhat surprised when reading your posts. You talk of "gravitomagnetism". This is the theory of Oliver Heaviside which he published in 1893 and it is the Maxwell-analogy for gravity. However, it is known that the general relativity theory is based upon a totally different set of premises than gravitomagnetism. Also, it is known that ...

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Yes. See Principles of Electrodynamics by Melvin Schwartz. He derives all electrodynamics including Maxwell's equations from Coulomb's Law and Special Relativity.

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Answer expected by following author's hints. \begin{align} \mathbf{L}_{eg} &= \dfrac{1}{4\pi}\int \mathbf{r'} \times \left [\mathbf{E} \times \mathbf{B} \right] d^3r'\\ & = \dfrac{1}{4\pi} \int \left [ \left (\mathbf{B.r'} \right)\mathbf{E} - \left (\mathbf{E . r'} \right) \mathbf{B} \right] d^3r'\\ & = \dfrac{1}{4\pi} \int \left [ \left ...

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By analogy (between $\mathbf{E}$ and $\mathbf{B}$ as they are pretty much equivalent) then the divergeance of $\mathbf{B}$ field wouldn't be 0 anymore, instead: $$\nabla \cdot \mathbf{B}= \frac{\rho_{\rm magnetic}}{\mu_0}$$ With $\rho_{\rm magnetic}$ the magnetic charge density, and $\mu_0$ the permeability in vacuum, to interpret it, the divergence of the ...

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