Classical and quantum instability of compact Cauchy horizons in two dimensions

The author studies a class of two-dimensional model spacetimes with compact Cauchy horizons; these models retain some of the key features of the four-dimensional problem. All of the model Cauchy horizons are classically unstable against scalar perturbations and the mechanism of instability is 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). Some specific conjectures on the four-dimensional problem are given.