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

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 57, Issue 2, 1998, Pages 1052-1056

  Cramer, Claes R ^a   Kay, Bernard S ^a  

^a UNIVERSITY OF YORK   (United Kingdom)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0009003384     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.57.1052     Document Type: Article

References (17)

1. K. S. Thorne, in 13th International Conference on General Relativity and Gravitation, edited by R. J. Gleiser, C. N. Kozameh, and O. M. Moreschi (Institute of Physics Publishing, Bristol, 1993), p. 295.
2. S. W. Hawking, Phys. Rev. D 46, 603 (1992).
3. W. A. Hiscock and D. A. Konkowski, Phys. Rev. D 26, 1225 (1982).
4. S. V. Sushkov, Class. Quantum Grav. 12, 1685 (1995).
5. S. V. Sushkov, Class. Quantum Grav. 14, 523 (1997).
6. S. V. Krasnikov, Phys. Rev. D 54, 7322 (1996).
7. We remark [cf. A. S. Wightman in Cargèse Lectures in Theoretical Physics: High Energy Electromagnetic Interactions and Field Theory, edited by M. Lévy (Gordon and Breach, New York, 1967), p. 171] that, because of infrared problems, for the massless field in two dimensions, for many states of interest, only expectation values of products of derivatives of the field exist (rather than of the field itself). Here, we still refer to such states as being “of Hadamard form” provided suitable derivatives of their two-point function are equal to the corresponding derivatives of the appropriate two-dimensional version (“(Formula presented)”) of the Hadamard form. [This is the point of view which will be adopted in a forthcoming paper by A. R. Borrott, C. R. Cramer, and B. S. Kay (unpublished)]. In 7, a distinction is made between such states and true Hadamard states and (in Sec. III B of 7) an example is constructed of a true Hadamard state (of the massless scalar field on two dimensional Misner space) with bounded stress-energy tensor. We remark that it is easy to see that the statement of the theorem in this paper also holds for this latter example.
8. T. Tanaka and W. A. Hiscock, Phys. Rev. D 52, 4503 (1995).
9. D. G. Boulware, Phys. Rev. D 46, 4421 (1992).
10. M. Visser, Phys. Rev. D 55, 5212 (1997).
11. L. Hörmander, The Analysis of Partial Differential Operators IV (Springer, Berlin, 1985).
12. B. S. Kay, M. J. Radzikowski, and R. M. Wald, Commun. Math. Phys. 183, 533 (1997).
13. M. Visser, Phys. Lett. B (to be published).
14. C. R. Cramer and B. S. Kay, Class. Quantum Grav. 13, L143 (1996).
15. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, England, 1973).
16. R. M. Wald, Quantum Field Theory in Curved Spacetime and Black Hole Thermodynamics (University of Chicago Press, Chicago, 1994).
17. C. R. Cramer (unpublished).