Thermal and two-particle stress-energy must be ill defined on the two-dimensional Misner space chronology horizon
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 states 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')∈(N∩IGH)×(N∩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.
- Publication:
-
Physical Review D
- Pub Date:
- January 1998
- DOI:
- 10.1103/PhysRevD.57.1052
- arXiv:
- arXiv:gr-qc/9708028
- Bibcode:
- 1998PhRvD..57.1052C
- Keywords:
-
- 04.62.+v;
- Quantum field theory in curved spacetime;
- General Relativity and Quantum Cosmology
- E-Print:
- 6 pages, LaTeX, RevTeX, no figures