Stress-energy must be singular on the Misner space horizon even for automorphic fields

We use the image sum method to reproduce Sushkov's result that for a massless automorphic field on the initial globally hyperbolic region IGH of Misner space, one can always find a special value of the automorphic parameter alpha such that the renormalized expectation value (alpha\T-ab\alpha) in the Sushkov state '(alpha\.\alpha)' (i.e. the automorphic generalization of the Hiscock-Konkowski state) vanishes. However, we shall prove by elementary methods that the conclusions of a recent general theorem of Kay, Radzikowski and Wald apply in this case. That is, for any value of cc and any neighbourhood N of any point b on the chronology horizon there exists at least one pair of non-null related points (x, x') is an element of (N boolean AND IGH) x (N boolean AND IGH) such that the renormalized two-point function of an automorphic field G(ten)(alpha)(x, x') in the Sushkov state is singular. In consequence (alpha\T-ab\alpha) (as well as other renormalized expectation values such as (alpha\phi(2)\alpha)) is necessarily singular on the chronology horizon. We point out that a similar situation (i.e. singularity on the chronology horizon) holds for states on Gott space and Grant space.