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

Mathematics – Logic

Scientific paper

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Relativity Theory

Scientific paper

We construct the energy-momentum tensor in Minkowskian space-time for Einstein's collisionless system of test particles moving in concentric circles and obtain the four-force necessary to preserve equilibrium. We derive a tensor field, 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 we show that the tensor field is a linearized Schwarzschild fieldwith a cosmological constant (this constant being the “potential energy” calculated on the surface of the sphere).

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