### EM+gravity framework for (quantized) topological charges

Posted:

**Thu Sep 02, 2021 9:14 pm**I have finally worked out mathematical framework up to Euler-Lagrange for this ellipsoid field/liquid crystal like approach: https://arxiv.org/pdf/2108.12359

- field of 3 distinguishable axes using 3x3 matrices preferring fixed set of eigenvalues,

- hedgehog of one of 3 axes for 3 leptons - charges governed by Maxwell equations, with magnetic dipole moment due to hairy ball theorem,

- then expanding to 4x4 matrices we get second set of Maxwell equations for GEM ( https://en.wikipedia.org/wiki/Gravitoelectromagnetism ).

They experimentally get long-range e.g. Coulomb-like interaction for topological charges in liquid crystals (e.g. https://www.nature.com/articles/s41598-017-16200-z ) - we can expand it to further particles and gravity.

The approach generalizes Faber's from vector to matrix field.

Electromagnetic (A vector, F tensor) are no longer just (connection Gamma, curvature R), but additionally include dependence of rotated shape (eigenvalues).

This way we can get vacuum dynamics of 3 strengths: EM >> pilot wave >> GEM.

I would gladly discuss.

- field of 3 distinguishable axes using 3x3 matrices preferring fixed set of eigenvalues,

- hedgehog of one of 3 axes for 3 leptons - charges governed by Maxwell equations, with magnetic dipole moment due to hairy ball theorem,

- then expanding to 4x4 matrices we get second set of Maxwell equations for GEM ( https://en.wikipedia.org/wiki/Gravitoelectromagnetism ).

They experimentally get long-range e.g. Coulomb-like interaction for topological charges in liquid crystals (e.g. https://www.nature.com/articles/s41598-017-16200-z ) - we can expand it to further particles and gravity.

The approach generalizes Faber's from vector to matrix field.

Electromagnetic (A vector, F tensor) are no longer just (connection Gamma, curvature R), but additionally include dependence of rotated shape (eigenvalues).

This way we can get vacuum dynamics of 3 strengths: EM >> pilot wave >> GEM.

I would gladly discuss.