The reliability horizon for semi-classical quantum gravity: Metric fluctuations are often more important than back-reaction

Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics

Volumn 415, Issue 1, 1997, Pages 8-14

  Visser, Matt ^a  

^a WASHINGTON UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001786841     PISSN: 03702693     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0370-2693(97)01226-4     Document Type: Article

References (31)

1. B.S. DeWitt, Quantum gravity: the new synthesis, in: S.W. Hawking, W. Israel (Eds.), General Relativity: An Einstein Centenary Survey, Cambridge University Press, Cambridge, 1979.
2. N.D. Birrell, P.C.W. Davies, Quantum fields in curved spacetime, Cambridge University Press, Cambridge, 1982.
3. S.A. Fulling, Aspects of quantum field theory in curved space-time, Cambridge University Press, Cambridge, 1989.
4. M. Visser, Lorentzian wormholes - from Einstein to Hawking, AIP Press, New York, 1995.
5. M.S. Morris, K.S. Thorne, Am. J. Phys. 56 (1988) 395.
6. M.S. Morris, K.S. Thorne, U. Yurtsever, Phys. Rev. Lett. 61 (1988) 1446.
7. M. Visser, Phys. Rev. D 39 (1989) 3182.
8. M. Visser, Nucl. Phys. B 328 (1989) 203.
9. S.W. Hawking, The Chronology Protection Conjecture, in: H. Sato (Ed.), Proceedings of the 6th Marcel Grossmann Meeting, Kyoto, Japan, June 23-29, 1991, World Scientific, Singapore, 1992.
10. S.W. Hawking, Phys. Rev. D 46 (1992) 603.
11. S.W. Kim, K.S. Thorne, Phys. Rev. D 43 (1991) 3929.
12. V.P. Frolov, Phys. Rev. D 43 (1991) 3878.
13. M. Visser, Phys. Rev. D 47 (1993) 554.
14. M. Visser, Nucl. Phys. B 416 (1994) 895.
15. B.S. Kay, M. Radzikowski, R.M. Wald, Quantum Field Theory on Spacetimes with a Compactly Generated Cauchy Horizon, gr-qc/9603012; Communications in Mathematical Physics 183 (1997) 533.
16. J.A. Wheeler, Phys. Rev. 97 (1955) 511.
17. J.A. Wheeler. Ann. Phys. (NY) 2 (1957) 604.
18. K.S. Thorne, R.H. Price, D.A. Macdonald (Eds.), Black holes: The membrane paradigm, Yale, New Haven, 1986.
19. S.V. Sushkov, Chronology protection and quantized fields: Complex automorphic scalar field in Misner space, gr-qc/9509056; Class. Quant. Grav. 14 (1997) 523.
20. S.V. Sushkov, Quantum complex scalar field in the two-dimensional space-time with closed timelike curves and a time machine problem, gr-qc/9410008; Class. Quant. Grav. 12 (1995) 1685.
21. S.V. Krasnikov, On the quantum stability of the time machine, gr-qc/9508038; Phys. Rev. D 54 (1996) 7322.
22. S.V. Krasnikov, Singularity free WEC respecting time machine; gr-qc/9702031.
23. M. Visser, Traversable wormholes: the Roman ring, gr-qc/9702043; Physical Review D 45 (1997) 5212.
24. C.R. Cramer, B.S. Kay, Stress-energy must be singular on the Misner space horizon even for automorphic fields, gr-qc/9606027; Class. Quant. Grav. 13 (1996) L143.
25. D.G. Boulware, Quantum field theory in spaces with closed timelike curves, hep-th/9207054; Physical Review D 46 (1992) 4421.
26. J.D. Grant, Cosmic strings and chronology protection, hepth/9209012; Physical Review D 47 (1993) 2388.
27. T. Tanaka, W.A. Hiscock, Massive scalar field in multiple connected spacetime, gr-qc/9504021; Physical Review D 52 (1995) 4503.
28. B. Kay, M. Radzikowski, R.M. Wald, private communication.
29. Earlier attempts at developing notions somewhat analogous to the reliability horizon can be found in [9, 10] and [11]. These early suggestions involve an undesirable observer dependence [4].
30. Kuo and Ford have previously suggested that fluctuations in the stress-energy tensor might invalidate the semi-classical approximation long before curvatures become large. See C.-I. Kuo, L.H. Ford, Phys Rev D 47 (1993) 4510. The difference here is that I am focussing on fluctuations in the metric, not the stress-energy. Even if stress-energy fluctuations are large this does not automatically mean that metric fluctuations must be large.
31. R.M. Wald, General Relativity, U. Chicago Press, Chicago, 1984, pp. 212-216, see esp. pp. 214-215.