The Cauchy problem on spacetimes containing CTCs#
One way to explore the compatibility between the semiclassical laws of physics and CTCs is to determine whether the two can be consolidated without having unacceptable causality violations manifest. A prominent method with which this can be accomplished is by looking at the Cauchy problem [5, 6] for relativistic classical scalar fields in spacetimes containing CTCs. In this problem, one seeks to, among other things, prove or disprove the existence of the field solutions to the relevant time-evolution equations of motion given initial data. By determining the nature of these solutions, we are able to formulate conclusive remarks regarding the affinity of the union of semiclassical field theory and CTCs.
Interestingly, research into the Cauchy problem in spacetimes with CTCs has yielded some perhaps unanticipated results given the seemingly restrictive requirement of self-consistency. Foremost are the findings [2, 2, 3, 3, 7, 8, 9, 10, 11, 12], which show that globally consistent time evolutions for free relativistic classical scalar fields with generic initial data (posed before any regions with CTCs) exist and are generally unique in certain classes of non-globally hyperbolic (including CTC) spacetimes. Consequently, at least in the context of non-interacting, classical scalar fields, CTCs appear to be robust and spacetimes containing them are not as pathological as one might have initially suspected.
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