On the Energy-Momentum Problem in Static Einstein Universe

The energy-momentum distributions of Einstein's simplest static geometrical model for an isotropic and homogeneous universe are evaluated. For this purpose, Einstein, Bergmann--Thomson, Landau--Lifshitz (LL), Moller and Papapetrou energy-momentum complexes are used in general relativity. While Einstein and Bergmann--Thomson complexes give exactly the same results, LL and Papapetrou energy-momentum complexes do not provide the same energy densities. The Moller energy-momentum density is found to be zero everywhere in Einstein's universe. Also, several spacetimes are the limiting cases considered here.