Symmetries of cosmological Cauchy horizons with exceptional orbits

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Abstract
We show here that if an analytic space-time satisfying the vacuum (or electrovacuum) Einstein equations contains a compact null hypersurface with closed generators, then the space-time must have a nontrivial Killing vector field. This result is an extension of an earlier theorem, which required that the generators of the hypersurface must not only be closed, but in addition must satisfy a local product bundle (LPB) condition. This LPB condition (which is known to be violated in certain of the Kerr–Taub–NUT space-time models) is equivalent to the requirement that the generators must all be ordinary fibers of a Seifert fibration. We prove here that the LPB condition can be dropped. Thus we have stronger support for our conjecture that causality violations (as evidenced by Cauchy horizons) in cosmological solutions of the Einstein equations are essentially an artifact of symmetry, and are therefore nongeneric.

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