Mathematics – Logic
Scientific paper
Nov 1978
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978gregr...9.1021h&link_type=abstract
General Relativity and Gravitation, Volume 9, Issue 11, pp.1021-1030
Mathematics
Logic
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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