Аннотация

The intrinsic metric symmetries of pseudo-Riemannian space-time universally reinforce strict spatial flatness in the GR metric formalism. The non-linear time element of the four-interval depends on the particle velocity, or spatial displacement, and differs from the proper-time rate of a local observer. The passive/active energy-charge for 1686, 1913, and 1915 gravitational laws maintains the universal free fall and the Principle of Equivalence for flat material space with the smooth radial metric. The observed planetary perihelion precession, the radar echo delay, and gravitational light bending can be explained by this metric solution quantitatively without departure from Euclidean spatial geometry. Non-Newtonian flat-space precessions are expected for non-point orbiting gyroscopes exclusively due to the GR inhomogenious time in the Earth's radial field. The self-contained Einstein relativity admits further geometrization of the r⁻⁴ radial particle for energy-to-energy gravitation in non-empty space without references to Newton's mass-to-mass attraction. The post-Newtonian inharmonic potential for distributed particle densities is also the exact solution to Maxwell's equations with the r⁻⁴ electric charge density for the (astro)electron.

Keywords: Non-empty space, 3D flatness, Radial energy-charges, Geometrization of continuous particles, Nonlocal energy-to-energy relativity