How did Einstein come to the conclusion that the energy tensor's components should be the following?
Why did he choose those elements (energy density and flux, momentum, shear stress, and pressure) and locations? Why density and not pure mass? Why pressure, and what is that? Why shear stress, and what is that? Why it is not included in mostly every important metric solution (Schwarzschild, Kerr...)? Energy flux because the movement of matter can alter the curvature along the displacement, as when happens heavily when two black holes collide? Is it the energy density flux or just raw energy? What is momentum density?
And finally, how does it relate to the metric and Ricci tensors? I suppose that $T_{00}=R_{00}-\dfrac{1}{2}g_{00}$. Does it mean that all the curvature would indeed recay in time curvature? It is clearly not the case. So how do you relate a big and disproportionare $T_{00}$ component with respect to others of the energy tensor with the other elements of Ricci and metric tensors?
