Einstein's static universe obeys ##\rho = 2\lambda##. So, attractive and repelling gravity cancel each other. I'm curious about the spacetime in this universe. Because the scale factor is constant, it seems that neighboring co-moving test particles don't show relative acceleration, thus no geodesic deviation. So, from this I would expect the spacetime to be flat. On the other side, as this universe contains energy, the spacetime can't be flat like Minkowski-spacetime. Obviously I am missing something and I will appreciate any help. Perhaps it is important to look at the 4x4 matrix of the stress-energy tensor describing the static universe. Unfortunately I couldn't find any reference. It seems correct to say that all matter particles are at rest to each other. If so, does it mean that the non-diagonal elements, representing shear stress and momentum flux would vanish?