It is well known that Einstein's Energy Stress Tensor only accounts for electromagnetic stress upon the gravitational medium which does not account for the other forces of nature, so we are going to experiment with changing the T00 section to account for the Strong Nuclear Force and Weak Nuclear Force in the Energy Density section of the Energy Stress Tensor.
First we must define what is Energy density which is Joules/Volume which are the units of Energy Density meaning any equation added to this Tensor must be in the form of Joules/Volume for the Strong and Weak Nuclear forces. Now gravity in energy is defined as Eg = EEM + ESNF + EWNF meaning that the energy is equal to the combined energy of all the forces taking those divided by volume gives Eg/V = EEM/V + ESNF/V + EWNF/V which V = (4/3)πr3 , so by taking all the parts of the equation divided by the 3-D space we can arrive at that Energy Density is just Energy potential divided by volume. The electromagnetic Density is already solved as EEM/ V= (1/2)(e0E2 + (1/u0)B2) Similar equations must be derived for the Strong and Weak Nuclear Forces for ESNF/V and EWNF/V.
The Strength of Charged particles bound by the Strong Nuclear Force is E = Ke2/r where as the binding energy between two Neutral particles is U = U0(r0/r)e-r/r0 we can create a any case for charged and neutral particles by adding these equations together ECharged + UNeutral = Ke2/r + U0(r0/r)e-r/r0 now the description for the Strong Nuclear Force is completed for charged and neutral particles. If the equation is divided by V = (4/3)πr3 ,we arrive at a energy density of (ECharged + UNeutral)/V = (3/4)(Ke2/r + U0(r0/r)e-r/r0)/πr3 which can now be added to the Tensor making (EEM + ESNF)V = (1/2)(e0E2 + (1/u0)B2) + (3/4)(Ke2/r + U0(r0/r)e-r/r0)/πr3 which is a accurate Energy Density for the Electromagnetic and Strong Nuclear Forces which is not complete yet as the WNF needs to be added, but for now T00 = (1/2)(e0E2 + (1/u0)B2) + (3/4)(Ke2/r + U0(r0/r)e-r/r0)/πr3 considering the Strong Nuclear Force and Electromagnetism.
The Weak Nuclear Force is a bit more tricky to get a energy density for as there is not a equation for the Energy of the WNF but it can be added as EWNF = Σ0NΔENucleon as a complex summation that counts the nucleon changes in energy via the weak nuclear force making this part of the equation like Gibb's Free Energy in enzyme reactions but counting for how many nucleons experience changes via the Weak Nuclear Force, as a energy density the equations is EWNF/V = Σ0NΔENucleon/(4/3)πr3 = (3/4)Σ0NΔENucleon/πr3 . This gives a accurate description of the energy density of a particle decay at a given time by summing the particle changes which can be added to T00 as T00 =(1/2)(e0E2 + (1/u0)B2) + (3/4)(Ke2/r + U0(r0/r)e-r/r0 + Σ0NΔENucleon)/πr3 which yields an equation that describes all the forces in the Energy Stress Tensor.
Unified General Relativity Energy Density
T00 =(1/2)(e0E2 + (1/u0)B2) + (3/4)(Ke2/r + U0(r0/r)e-r/r0 + Σ0NΔENucleon)/πr3
Edited by VictorMedvil, 07 January 2020 - 10:59 AM.