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

TY - JOUR

T1 - Stress - energy must be singular on the Misner space horizon even for automorphic fields

AU - Cramer, Claes

AU - Kay, Bernard S.

PY - 1996/12

Y1 - 1996/12

N2 - 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 such that the renormalized expectation value in the Sushkov state `' (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 and any neighbourhood N of any point b on the chronology horizon there exists at least one pair of non-null related points such that the renormalized two-point function of an automorphic field in the Sushkov state is singular. In consequence (as well as other renormalized expectation values such as ) 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.

AB - 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 such that the renormalized expectation value in the Sushkov state `' (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 and any neighbourhood N of any point b on the chronology horizon there exists at least one pair of non-null related points such that the renormalized two-point function of an automorphic field in the Sushkov state is singular. In consequence (as well as other renormalized expectation values such as ) 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.

U2 - 10.1088/0264-9381/13/12/002

DO - 10.1088/0264-9381/13/12/002

M3 - Article

SN - 1361-6382

VL - 13

SP - L143-L149

JO - Classical and Quantum Gravity

JF - Classical and Quantum Gravity

IS - 12

ER -