gio06 , you are probably familiar with the DTS idea of Cardone and the late Mignani, they sustain the Minkowski Spacetime is anisotropic, or can be made anisotropic by way of energy. I just mention it because you are using it as starting point.
I
Any anisotropy in Minkowsi spacetime implies that the Vacuum is structured as experimentally confirmed by the Aharonov-Bohm effect. A four-vector field [electromagnetic four potential] can be used to represent the structure of the Vacuum.
Aharonov-bohm effect as the basis of electromagnetic energy inherent in the vacuum - Foundations of Physics Letters
The Aharonov-Bohm effect shows that the vacuum is structured, and that there can exist a finite vector potentialA in the vacuum when the electric field…
link.springer.com