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Thermal and two-particle stress-energy must be ill defined on the two-dimensional Misner space chronology horizon

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JournalPhysical Review D
DatePublished - 15 Jan 1998
Issue number2
Volume57
Number of pages5
Pages (from-to)1052-1056
Original languageEnglish

Abstract

We show that an analogue of the (four-dimensional) image sum method can be used to reproduce the results, due to Krasnikov, that for the model 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 these stares vanishes on IGH. However, we shall prove that the conclusions 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 two-point function is singular. (We prove this by showing that the two-point functions of these states share the same singularities as the conformal vacuum on which they are built.) In other words, the stress-energy tensor in any of these states is necessarily ill defined on the Cauchy horizon.

    Research areas

  • TIME-LIKE CURVES, SCALAR FIELD, QUANTUM

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