376(3): The Self Consistent equations of ECE2 Gravitostatics

These are the lagrangian (1), the Minkowski-like force equation (15), the ECE2 covariant Euler Lagrange equation (13) in which the proper time appears, and the ECE2 covariant field equations (18) to (21). The field equations are of course automatically relativistic. In Cartesian coordinates they give Eqs. (35) to (42), which can be simplifed as described. The field equations can be reduced to one Cartesian Eq. (53). The precessing orbit is given by solving Eqs. (37) and (38) simultaneously, i.e. by solving the Minkowski-like force equation, the ECE2 covariant Newton equation. So everything is correctly relativistic and self consistent. All these equations are written in a spacetime with finite torsion and curvature. In ECE2 gravitostatics the mass density of the source (the sun for example) must be independent of time. So ECE2 gravitostatics does not produce gravitational radiation, because for gravitational radiation one needs the magnetogravitational field and gravitational Ampere Maxwell equation and gravitational Faraday law, together with the magnetogravitational Gauss law. All these equations hold for electrostatics and can be solved by computer in exactly the same way. Major advances are being made now at a rapid pace. Einsteinian general relativity is nowhere used. Finally the spin connection can be found from these equations. In special relativity there is of course no spin connection.


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