THERMAL AND 2-PARTICLE STRESS-ENERGY MUST BE ILL-DEFINED ON THE 2-DIMENSIONAL MISNER SPACE CHRONOLOGY HORIZON

We show that an analogue of the (four-dimensional) image sum method ca n be used to reproduce the results, due to Krasnikov, that for the mod el of a real massless scalar field on the initial globally hyperbolic (IGH) region of two-dimensional Misner space there exist two-particle and thermal Hadamard states (built on the conformal vacuum) such that the (expectation value of the renormalised) stress-energy tensor in th ese stares vanishes on IGH. However, we shall prove that the conclusio ns of a general theorem by Kay, Radzikowski, and Wald still apply for these states. That is, in any of these states, for any point b on the Cauchy horizon and any neighbourhood N of b, there exists at least one pair of non-null related points (x,x')epsilon(N boolean AND IGH) x (N boolean AND IGH) such that (a suitably differentiated form of) its tw o-point function is singular. (We prove this by showing that the two-p oint functions of these states share the same singularities as the con formal vacuum on which they are built.) In other words, the stress-ene rgy tensor in any of these states is necessarily ill defined on the Ca uchy horizon.