Negative Energy Densities in Extended Sources Generating Closed Timelike Curves in General Relativity with and without Torsion

Near a spinning point particle in (2+1)-dimensional gravity (or near an infinitely thin, straight, spinning string in 3+1 dimensions) there is a region of space-time with closed timelike curves. Exact solutions for extended sources with apparently physically acceptable energy-momentum tensors, have produced the same exterior space-time structure. Here it is pointed out that in the case with torsion, closed timelike curves appear only for spin densities so high that the spin energy density is higher than the net effective energy density. In models without torsion, the presence of closed time-like curves is related to a heat flow of unphysical magnitude. This corroborates earlier arguments against the possibility of closed timelike curves in space-time geometries generated by physical sources.

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