COSMIC STRINGS AND CHRONOLOGY PROTECTION

A space consisting of two rapidly moving cosmic strings has recently been constructed by Gott that contains closed timelike curves. The global structure of this space is analyzed and it is found that, away from the strings, the space is identical to a generalized Misner space. The vacuum expectation value of the energy-momentum tensor for a conformally coupled scalar field is calculated on this generalized Misner space. It is found to diverge very weakly on the chronology horizon, but more strongly on the polarized hypersurfaces. The divergence on the polarized hypersurfaces is strong enough that when the proper geodesic interval around any polarized hypersurface is of the order of the Planck length squared, the perturbation to the metric caused by the back reaction will be of the order one. Thus we expect the structure of the space will be radically altered by the back reaction before quantum gravitational effects become important. This suggests that Hawking's ''chronology protection conjecture'' holds for spaces with a noncompactly generated chronology horizon.