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Black Holes and Running Couplings: A Comparison of Two Complementary Approaches

  • Benjamin KochEmail author
  • Carlos Contreras
  • Paola Rioseco
  • Frank Saueressig
Chapter
Part of the Springer Proceedings in Physics book series (SPPHY, volume 170)

Abstract

Black holes appear as vacuum solutions of classical general relativity which depend on Newton’s constant and possibly the cosmological constant. At the level of a quantum field theory, these coupling constants typically acquire a scale-dependence. A quantum treatment of a black hole should thus take this effect into account. In these proceedings we briefly summarize two complementary approaches to this problem: the renormalization group improvement of the classical solution based on the scale-dependent gravitational couplings obtained within the gravitational Asymptotic Safety program and the exact solution of the improved equations of motion including an arbitrary scale dependence of the gravitational couplings. Remarkably the picture of the “quantum black holes” obtained from these very different improvement strategies is strikingly similar.

Notes

Acknowledgments

The work of B.K. was supported proj. Fondecyt 1120360 and anillo Atlas Andino 10201; the research of F.S. is supported by the Deutsche Forschungsgemeinschaft (DFG) within the Emmy-Noether program (Grant SA/1975 1-1). The work of C.C. was supported proj. Fondecyt 1120360 and DGIP grant 11.11.05.

References

  1. 1.
    K.S. Stelle, Phys. Rev. D 16, 953 (1977)MathSciNetCrossRefADSGoogle Scholar
  2. 2.
    J. Julve, M. Tonin, Nuovo Cim. B 46, 137 (1978)MathSciNetCrossRefADSGoogle Scholar
  3. 3.
    E.S. Fradkin, A.A. Tseytlin, Phys. Lett. B 104, 377 (1981)Google Scholar
  4. 4.
    E.S. Fradkin, A.A. Tseytlin, Nucl. Phys. B 201, 469 (1982)Google Scholar
  5. 5.
    I.G. Avramidi, A.O. Barvinsky, Phys. Lett. B 159, 269 (1985)CrossRefADSGoogle Scholar
  6. 6.
    N.H. Barth, S.M. Christensen, Phys. Rev. D 28, 1876 (1983)MathSciNetCrossRefADSGoogle Scholar
  7. 7.
    G. de Berredo-Peixoto, I.L. Shapiro, Phys. Rev. D 71, 064005 (2005). arXiv:hep-th/0412249
  8. 8.
    A. Codello, R. Percacci, Phys. Rev. Lett. 97, 221301 (2006). arXiv:hep-th/0607128
  9. 9.
    M. Niedermaier, Phys. Rev. Lett. 103, 101303 (2009)CrossRefADSGoogle Scholar
  10. 10.
    K. Groh, S. Rechenberger, F. Saueressig, O. Zanusso, PoS EPS -HEP2011, 124 (2011). arXiv:1111.1743
  11. 11.
    M. Niedermaier, M. Reuter, Living Rev. Rel. 9, 5 (2006)Google Scholar
  12. 12.
    R. Percacci, in Approaches to Quantum Gravity: Towards a New Understanding of Space, Time and Matter, ed. by D. Oriti (Cambridge University Press, Cambridge, 2009). arXiv:0709.3851
  13. 13.
    A. Codello, R. Percacci, C. Rahmede, Int. J. Mod. Phys. A 23, 143 (2008). arXiv:0705.1769
  14. 14.
    M. Reuter, F. Saueressig, New J. Phys. 14, 055022 (2012). arXiv:1202.2274
  15. 15.
    A. Bonanno, M. Reuter, Phys. Rev. D 60, 084011 (1999). arXiv:gr-qc/9811026
  16. 16.
    A. Bonanno, M. Reuter, Phys. Rev. D 62, 043008 (2000). arXiv:hep-th/0002196
  17. 17.
  18. 18.
    A. Bonanno, M. Reuter, Phys. Rev. D 73, 083005 (2006). arXiv:hep-th/0602159
  19. 19.
    B. Koch, Phys. Lett. B 663, 334 (2008). arXiv:0707.4644
  20. 20.
    T. Burschil, B. Koch, Zh Eksp, Teor. Fiz. 92, 219 (2010). arXiv:0912.4517
  21. 21.
    M. Reuter, E. Tuiran. arXiv:hep-th/0612037
  22. 22.
    M. Reuter, E. Tuiran, Phys. Rev. D 83, 044041 (2011). arXiv:1009.3528
  23. 23.
    K. Falls, D.F. Litim, A. Raghuraman, Int. J. Mod. Phys. A 27, 1250019 (2012). arXiv:1002.0260
  24. 24.
    K. Falls, D.F. Litim. arXiv:1212.1821
  25. 25.
    D.F. Litim, K. Nikolakopoulos. arXiv:1308.5630
  26. 26.
    R. Casadio, S.D.H. Hsu, B. Mirza, Phys. Lett. B 695, 317 (2011). arXiv:1008.2768
  27. 27.
    M. Reuter, H. Weyer, Phys. Rev. D 69, 104022 (2004). arXiv:hep-th/0311196
  28. 28.
    B. Koch, F. Saueressig, Class. Quant. Grav. (to Appear). arXiv:1306.1546
  29. 29.
    S. Weinberg, in General Relativity, an Einstein Centenary Survey, eds. by S.W. Hawking, W. Israel (Cambridge University Press, Cambridge, 1979)Google Scholar
  30. 30.
    M. Reuter, Phys. Rev. D 57, 971 (1998). arXiv:hep-th/9605030
  31. 31.
    M. Reuter, F. Saueressig, Phys. Rev. D 65, 065016 (2002). arXiv:hep-th/0110054
  32. 32.
    C. Contreras, B. Koch, P. Rioseco, Class. Quant. Grav. 30, 175009 (2013). arXiv:1303.3892
  33. 33.
    M. Reuter, H. Weyer, JCAP 0412, 001 (2004). arXiv:hep-th/0410119
  34. 34.
    S. Domazet, H. Stefancic, Class. Quant. Grav. 29, 235005 (2012). arXiv:1204.1483

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Benjamin Koch
    • 1
    Email author
  • Carlos Contreras
    • 2
  • Paola Rioseco
    • 1
  • Frank Saueressig
    • 3
  1. 1.Instituto de FisicaPontificia Universidad Católica de ChileSantiagoChile
  2. 2.Departamento de FísicaUniversidad Técnica Federico Santa MaríaValparaísoChile
  3. 3.Institute for Mathematics, Astrophysics and Particle PhysicsRadboud UniversityNijmegenThe Netherlands

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