A reconstruction in Minkowskian space-time of Einstein's assembly of test particles

The energy-momentum tensor in Minkowskian space-time for Einstein's collisionless system of test particles moving in concentric circles is constructed and the four-force necessary to preserve equilibrium obtained. A tensor field is derived satisfying the linearized Einstein equations, which is consistent with the applied four-force. If the particles are contained within a sphere, then outside the sphere it is shown that the tensor field is a linearized Schwarzschild field with a cosmological constant (this constant being the 'potential energy' calculated on the surface of the sphere). (author)