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Renormalized graviton stress-energy tensor in curved vacuum space-times

B. Allen, A. Folacci, and A. C. Ottewill

  • Groupe d’Astrophysique Relativiste, Centre National de la Recherche Scientifique, Observatoire de Paris(enMeudon, 92195 Meudon, France

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Phys. Rev. D 38, 1069 – Published 15 August, 1988

DOI: https://doi.org/10.1103/PhysRevD.38.1069

Abstract

The graviton contribution to the renormalized one-loop effective stress-energy tensor is calculated in an arbitrary vacuum space-time with a cosmological constant. This is done for (1) the standard definition of the effective action and (2) the reparametrization-invariant effective action of Vilkovisky and DeWitt. The renormalized one-loop effective stress-energy tensor is given in terms of the graviton two-point function, by making use of its symmetric Hadamard representation.

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References (25)

  1. G. A. Vilkovisky, in The Quantum Theory of Gravity, edited by S. M. Christensen (Hilger, London, 1984); Nucl. Phys. B234, 125 (1984).
  2. E. S. Fradkin and A. A. Tseytlin, Nucl. Phys. B234, 509 (1984).
  3. A. O. Barvinsky and G. A. Vilkovisky, Phys. Rep. 119, 1 (1985).
  4. S. R. Huggins, G. Kunstatter, H. P. Leivo and D. J. Toms, Phys. Rev. Lett. 58, 296 (1987).
  5. A. Rebhan, Nucl. Phys. B228, 832 (1987).
  6. B. S. DeWitt, in Quantum Field Theory and Quantum Statistics, edited by I. A. Batelin, C. J. Isham, and G. A. Vilkovisky (Hilger, Bristol, 1987).
  7. M. R. Brown and A. C. Ottewill, Proc. R. Soc. London A389, 379 (1983).
  8. M. R. Brown and A. C. Ottewill, Phys. Rev. D 34, 1776 (1986).
  9. D. Bernard and A. Folacci, Phys. Rev. D 34, 2286 (1986).
  10. R. M. Wald, Commun. Math. Phys. 54, 1 (1977); Phys. Rev. D 17, 1477 (1978).
  11. S. L. Adler, J. Lieberman and Y. G. Ng, Ann. Phys. (N.Y.) 106, 279 (1977); S. L. Adler and J. Lieberman, ibid. 113, 294 (1978).
  12. S. W. Hawking and G. F. R. Ellis, The Large Scale Structure of Space-Time (Cambridge University Press, Cambridge, England, 1973).
  13. S. M. Christensen and N. H. Barth, Phys. Rev. D 28, 1876 (1983). (Note the sign error in LAMBDA in Appendix D.)
  14. J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations (Yale University Press, New Haven, CT, 1923).
  15. B. S. DeWitt and R. W. Brehme, Ann. Phys. (N.Y.) 9, 220 (1960).
  16. J. H. Van Vleck, Proc. Natl. Acad. Sci. U.S.A. 14, 178 (1928); C. Morette, Phys. Rev. 81, 848 (1951).
  17. B. S. DeWitt, Dynamical Theory of Groups and Fields (Gordon and Breach, New York, 1965).
  18. A. H. Najmi and A. C. Ottewill, Phys. Rev. D 32, 1942 (1985).
  19. N. D. Birrell and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, England, 1982).
  20. B. S. DeWitt, in Relativity, Groups and Topology II, proceedings of the Les Houches Summer School, Les Houches, France, 1983 (Les Houches Summer School Proceedings, Vol. 40), edited by B. S. DeWitt and R. Stora (North-Holland, Amsterdam, 1984).
  21. S. M. Christensen, Phys. Rev. D 17, 946 (1978).
  22. S. M. Christensen, Phys. Rev. D 14, 2490 (1976).
  23. J. L. Synge, Relativity: The General Theory (North-Holland, Amsterdam, 1960).
  24. P. Garabedian, Partial Differential Equations (Wiley, New York, 1964).
  25. S. N. Gupta, Proc. Phys. Soc. London A63, 46 (1950); ibid. A65, 161 (1952).

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Phys. Rev. D 38, 1069– Published 15 August, 1988
  • Received 3 December 1987

© 1988 American Physical Society

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