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.
| Original language | English |
|---|---|
| Pages (from-to) | 1052-1056 |
| Number of pages | 5 |
| Journal | Physical Review D |
| Volume | 57 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 15 Jan 1998 |
Keywords
- TIME-LIKE CURVES
- SCALAR FIELD
- QUANTUM