Research on Geometry of Gravitation by Distinguishing Between Spatial and Temporal Part of Spherically Symmetric Metric - Trenčevski, Kostadin; Celakoska, Emilija (Communications in Mathematics and Applications, 2025)
We prove a theorem that in case of a spherically symmetric metric the curvature tensor of the spatial metric (by ignoring the temporal component) must be 0, because otherwise it leads to a paradox. We consider gravitation, assuming that a point-mass body with mass \(M\) radially translates each point by a 3-vector with magnitude \(GM/c^2\). The temporal metric coefficient \(g_44\) is uniquely determined by \(g\), so the Riemann curvature tensor is non-zero. The experimental tests apply and the basic results remain the same as in GR. The obtained equations for \(n\)-body problem differ from the Einstein-Infeld-Hoffmann equations by Lorentz invariant addends. While in GR the curvature scalar \(R\) is proportional to the density of matter, here \(R\) is proportional to the density of energy and also to the density of matter.