Virtual black holes in generalized dilaton theories

theoretical physics

Abstract.

The virtual black hole phenomenon, which has been observed previously in specific models, is established for generic 2D dilaton gravity theories with scalar matter. The ensuing effective line element can become asymptotically flat only for two classes of models; among them spherically reduced theories and the string inspired dilaton black hole. We present simple expressions for the lowest order scalar field vertices of the effective theory which one obtains after integrating out geometry exactly. Treating the boundary in a natural and simple way, asymptotic states, tree-level vertices and the tree-level S-matrix are conformally invariant. Examples are provided pinpointing the physical consequences of virtual black holes on the (CPT-invariant) S-matrix for gravitational scattering of scalar particles. For minimally coupled scalars the evaluation of the S-matrix in closed form is straightforward. For a class of theories including the string inspired dilation black hole all tree-graph vertices vanish, which explains the particular simplicity of that model and at the same time shows yet another essential difference to the Schwarzschild case.

Keywords

Black Hole Scalar Matter Order Scalar Dilaton Black Hole Dilaton Gravity 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Grumiller, W. Kummer, D.V. Vassilevich, Phys. Rept. 369, 327, 429 (2002), hep-th/0204253CrossRefMATHGoogle Scholar
  2. 2.
    C.G. Callan, Jr., S.B. Giddings, J.A. Harvey, A. Strominger, Phys. Rev. D 45, 1005 (1992), hep-th/9111056CrossRefGoogle Scholar
  3. 3.
    D. Cangemi, R. Jackiw, Phys. Rev. Lett. 69, 233 (1992), hep-th/9203056CrossRefMathSciNetMATHGoogle Scholar
  4. 4.
    F. Haider, W. Kummer, Int. J. Mod. Phys. A 9, 207 (1994)MathSciNetMATHGoogle Scholar
  5. 5.
    W. Kummer, H. Liebl, D.V. Vassilevich, Nucl. Phys. B 544, 403 (1999), hep-th/9809168CrossRefMathSciNetMATHGoogle Scholar
  6. 6.
    D. Grumiller, W. Kummer, D.V. Vassilevich, Nucl. Phys. B 580, 438 (2000), gr-qc/0001038CrossRefMathSciNetMATHGoogle Scholar
  7. 7.
    P. Fischer, Phys. Lett. B 521, 357 (2001), gr-qc/0105034CrossRefMathSciNetMATHGoogle Scholar
  8. 8.
    D. Grumiller, Class. Quant. Grav. 19, 997 (2002), gr-qc/0111097CrossRefMathSciNetMATHGoogle Scholar
  9. 9.
    K. Kuchař, Phys. Rev. D 4, 955 (1971)CrossRefGoogle Scholar
  10. 10.
    P. Hajicek, C. Kiefer, Nucl. Phys. B 603, 531 (2001), hep-th/0007004CrossRefMathSciNetMATHGoogle Scholar
  11. 11.
    I. Kouletsis, P. Hajicek, gr-qc/0112062Google Scholar
  12. 12.
    V. Frolov, P. Sutton, A. Zelnikov, Phys. Rev. D 61, 024021 (2000), hep-th/9909086CrossRefGoogle Scholar
  13. 13.
    W. Kummer, D.V. Vassilevich, Annalen Phys. 8, 801 (1999), gr-qc/9907041CrossRefMathSciNetMATHGoogle Scholar
  14. 14.
    S.W. Hawking, Phys. Rev. D 53, 3099 (1996), hep-th/9510029CrossRefMathSciNetGoogle Scholar
  15. 15.
    W. Kummer, D.J. Schwarz, Nucl. Phys. B 382, 171 (1992)CrossRefMathSciNetMATHGoogle Scholar
  16. 16.
    W. Kummer, P. Widerin, Phys. Rev. D 52, 6965 (1995), gr-qc/9502031CrossRefMathSciNetGoogle Scholar
  17. 17.
    D. Grumiller, W. Kummer, Phys. Rev. D 61, 064006 (2000), gr-qc/9902074CrossRefGoogle Scholar
  18. 18.
    H. Balasin, H. Nachbagauer, Class. Quant. Grav. 11, 1453 (1994), gr-qc/9312028CrossRefMathSciNetGoogle Scholar
  19. 19.
    M.O. Katanaev, I.V. Volovich, Phys. Lett. B 175, 413 (1986)CrossRefMathSciNetGoogle Scholar
  20. 20.
    D.V. Vassilevich, A. Zelnikov, Nucl. Phys. B 594, 501 (2001), hep-th/0009084CrossRefMathSciNetMATHGoogle Scholar
  21. 21.
    D. Grumiller, Int. J. Mod. Phys. A 17, 989 (2001), hep-th/0111138Google Scholar
  22. 22.
    R.F. Streater, A.S. Wightman, PCT, spin and statistics, and all that (Advanced book classics) (Addison-Wesley, Redwood City 1989) Google Scholar
  23. 23.
    D. Grumiller, D. Hofmann, W. Kummer, Mod. Phys. Lett. A 16, 1597 (2001), gr-qc/0012026CrossRefGoogle Scholar
  24. 24.
    G.T. Horowitz, D. Marolf, Phys. Rev. D 52, 5670 (1995), gr-qc/9504028CrossRefMathSciNetGoogle Scholar
  25. 25.
    M.O. Katanaev, W. Kummer, H. Liebl, Phys. Rev. D 53, 5609 (1996), gr-qc/9511009CrossRefMathSciNetGoogle Scholar
  26. 26.
    A. Fabbri, J.G. Russo, Phys. Rev. D 53, 6995 (1996), hep-th/9510109CrossRefMathSciNetGoogle Scholar
  27. 27.
    Y. Uehara, Virtual black holes at linear colliders, hep-ph/0205068Google Scholar
  28. 28.
    S.B. Giddings, S. Thomas, Phys. Rev. D 65, 056010 (2002), hep-ph/0106219CrossRefGoogle Scholar
  29. 29.
    D. Grumiller, W. Kummer, D.V. Vassilevich, Positive specific heat of the quantum corrected dilaton black hole, hep-th/0305036Google Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.Institut für Theoretische PhysikTechnische Universität WienWienAustria
  2. 2.Institut für Theoretische PhysikMax-Planck-Institut für Mathematik in den NaturwissenschaftenLeipzigGermany

Personalised recommendations