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 α such that the renormalized expectation value 〈α|Tab|α〉 in the Sushkov state “〈α| · |α〉” (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-Wald apply in this case. I.e. for any value of α 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) ∈ (N ∩IGH)× (N ∩IGH) such that the renormalized two-point function of an automorphic field Gren(x, x ) in the Sushkov state is singular. In consequence 〈α|Tab|α〉 (as well as other renormalized expectation values such as 〈α|φ|α〉) 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. PACS numbers: 04.62.+v There has recently been interest in quantum field theory on spacetimes with a chronology horizon. (See [1, 2, 3] and references therein.) The reason for this interest is that these spacetimes (or rather those for which the chronology horizon is compactly generated [2]) are models for spacetimes in which time machines get manufactured. Hawking [2] has proposed the Chronology Protection Conjecture according to which the laws of physics (and in particular quantum effects) prevent such spacetimes from being physically realizable. In fact, there were arguments due to email:[email protected] email:[email protected]