Energy Momentum Tensor Generates Repulsive Gravitational Force

Branko M. Novakovic

Solution of the field equations by including gravitational energy – momentum tensor in it (but without cosmological constant Λ) generates repulsive gravitational force. This repulsive force could be the source of the dark energy. Regularity condition of the related line element gives the limitations to the gravitational radius GM/2c² ≤ r < ∞. This means that presented solution has no singularity points. Minimal diameter of the universe mass 2r = GM/c² corresponds to the Planck’s length L_pl = GM_pl /c², as the minimal diameter of the Planck’s mass M_pl.  From the universe velocity equation, we obtain the limitations to the energy conservation constant 0 < κ ≤ 1. This means that the kinetic energy is less or equal to the potential energy. For that case the spatial curvature of the space is ≥ 0. In other words, our universe is a flat or a hyperspherical, because hyperbolic universe is excluded. Further, the zero points of the universe velocity equation determine the minimal gravitational radius at r_min = GM/(1+κ)c² and maximal gravitational radius at r_max = GM/(1-κ)c². Applying radial density ρ_r = M/r to the minimal and maximal gravitational radiuses we obtain the other limitations to the energy conservation constant 0 < κ < 1 and to the spatial curvature of the space > 0.  In that case our universe is a hyperspherical because flat and hyperbolic universes are excluded by the mentioned limitations.

https://doi.org/10.31871/IJNTR.5.11.25