Hawking radiation and interacting fields

Regular Article


Hawking radiation is generally derived using a non-interacting field theory. Some time ago, Leahy and Unruh showed that, in two dimensions with a Schwarzschild geometry, a scalar field theory with a quartic interaction gets the coupling switched off near the horizon of the black hole. This would imply that interaction has no effect on Hawking radiation and free theory for particles can be used. Recently, a set of exact classical solutions for the quartic scalar field theory has been obtained. These solutions display a massive dispersion relation even if the starting theory is massless. When one considers the corresponding quantum field theory, this mass gap becomes a tower of massive excitations and, at the leading order, the theory is trivial. We apply these results to Hawking radiation for a Kerr geometry and prove that the Leahy-Unruh effect is at work. Approaching the horizon the scalar field theory has the mass gap going to zero. We devise a technique to study the interacting scalar theory very near the horizon increasing the coupling. As these solutions are represented by a Fourier series of plane waves, Hawking radiation can be immediately obtained with well-known techniques. These results open a question about the behavior of the Standard Model of particles very near the horizon of a black hole where the interactions turn out to be switched off and the electroweak symmetry could be restored.


  1. 1.
    S.W. Hawking, Nature 248, 30 (1974)ADSCrossRefGoogle Scholar
  2. 2.
    S.W. Hawking, Commun. Math. Phys. 43, 199 (1975) 46ADSCrossRefGoogle Scholar
  3. 3.
    V. Mukhanov, S. Winitzki, Introduction to Quantum Effects in Gravity (Cambridge University Press, Cambridge, UK, 2007)Google Scholar
  4. 4.
    L.E. Parker, D.J. Toms, Quantum Field Theory in Curved Spacetimes (Cambridge University Press, Cambridge, 2009)Google Scholar
  5. 5.
    M.K. Parikh, F. Wilczek, Phys. Rev. Lett. 85, 5042 (2000) hep-th/9907001ADSCrossRefGoogle Scholar
  6. 6.
    C. Corda, Eur. Phys. J. C 73, 2665 (2013) arXiv:1210.7747 [gr-qc]ADSCrossRefGoogle Scholar
  7. 7.
    C. Corda, S.H. Hendi, R. Katebi, N.O. Schmidt, JHEP 06, 008 (2013) arXiv:1305.3710 [gr-qc]ADSCrossRefGoogle Scholar
  8. 8.
    D.A. Leahy, W.G. Unruh, Phys. Rev. D 28, 694 (1983)ADSCrossRefGoogle Scholar
  9. 9.
    G. Collini, V. Moretti, N. Pinamonti, Lett. Math. Phys. 104, 217 (2014) arXiv:1302.5253 [gr-qc]CrossRefGoogle Scholar
  10. 10.
    H.S. Vieira, V.B. Bezerra, C.R. Muniz, Ann. Phys. 350, 14 (2014) arXiv:1401.5397 [gr-qc]ADSCrossRefGoogle Scholar
  11. 11.
    T. Damour, R. Ruffini, Phys. Rev. D 14, 332 (1976)ADSCrossRefGoogle Scholar
  12. 12.
    S. Sannan, Gen. Relativ. Gravit. 20, 239 (1988)ADSCrossRefGoogle Scholar
  13. 13.
    M. Frasca, J. Nonlinear Math. Phys. 18, 291 (2011) arXiv:0907.4053 [math-ph]ADSCrossRefGoogle Scholar
  14. 14.
    M. Frasca, Eur. Phys. J. C 74, 2929 (2014) arXiv:1306.6530 [hep-ph]ADSCrossRefGoogle Scholar
  15. 15.
    F.W.J. Olver, D.W. Lozier, R.F. Boisvert, C.W. Clark (Editors), NIST Handbook of Mathematical Functions (Cambridge University Press, New York, NY, 2010)Google Scholar
  16. 16.
    J.D. Jackson, Classical Electrodynamics (Wiley, Hoboken, USA, 1999)Google Scholar
  17. 17.
    C.W. Misner, K.S. Thorne, J.A. Wheeler, Gravitation (W.H. Freeman and Company, San Francisco, 1973)Google Scholar
  18. 18.
    R.H. Boyer, R.W. Lindquist, J. Math. Phys. 8, 265 (1967)ADSCrossRefGoogle Scholar
  19. 19.
    W.G. Unruh, N. Weiss, Phys. Rev. D 29, 1656 (1984)ADSCrossRefGoogle Scholar
  20. 20.
    M. Frasca, Mod. Phys. Lett. A 22, 1293 (2007) hep-th/0702056ADSCrossRefGoogle Scholar
  21. 21.
    M. Frasca, Int. J. Mod. Phys. A 23, 299 (2008) arXiv:0704.1568 [hep-th]ADSCrossRefGoogle Scholar
  22. 22.
    J.Y. Zhang, Z. Zhao, Phys. Lett. B 618, 14 (2005)ADSCrossRefGoogle Scholar
  23. 23.
    M. Frasca, Phys. Rev. D 73, 027701 (2006) 73ADSCrossRefGoogle Scholar

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