CLASSICAL AND QUANTUM INSTABILITY OF COMPACT CAUCHY HORIZONS IN 2 DIMENSIONS

Previously it was shown that, with appropriate relative motion of the wormhole mouths, an asymptotically flat wormhole spacetime can be made to evolve closed timelike curves (CTCs), starting from an initial partial Cauchy surface which does not admit any CTCs in its vicinity. The null surface that separates the region with CTCs from the initial causal region of spacetime is a Cauchy horizon. It is believed that, at least for some range of parameters for the model, this horizon is classically stable. Nevertheless, arguments have recently been made to suggest that the horizon has a quantum-field-theoretical instability that leads to unbounded vacuum polarization in its neighbourhood. Here we will attempt to clarify these issues by studying a class of two-dimensional model spacetimes with compact Cauchy horizons; these models retain some of the key features of the four-dimensional problem. We find that all of our model Cauchy horizons are classically unstable against scalar perturbations, and identify the mechanism of instability as the infinite blue-shifting of radiation near the horizon. The quantum instability of the horizon is purely non-radiative (particle creation remains bounded), and has exactly the same mechanism as in the classical case (infinite blue-shifting of the Casimir vacuum energy). Motivated partly by these results, we present some specific conjectures on the four-dimensional problem in the concluding section of the paper.