Quantum Field Theory in Non-globally Hyperbolic Space-Times
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Although it has been known for a long time that causality violation is not a priori ruled out by General Relativity, its investigation became a concerted effort only about a decade ago. This may have been prompted by the realization that if a “wormhole” could be created it would be possible to build a “time machine” (a space-time with compact achronal region). It has turned out to be surprisingly difficult to prove the physical impossibility of such space-times (as most relativists would want to have it). The most convincing argument in this direction rests on the semiclassical instability of the Cauchy horizon (i.e. a divergent 〈T μν〉 at the boundary of the achronal region) and underlies the “chronology protection conjecture” of Hawking (1992). But even if this is taken for granted, microscopic closed time-like curves may be allowed in quantum gravity. One is then led to consider as a tractable model problem quantum field theory on a background space-time with closed time-like curves.