Communications in Mathematical Physics

, Volume 127, Issue 2, pp 273–284 | Cite as

On the derivation of Hawking radiation associated with the formation of a black hole

  • Klaus Fredenhagen
  • Rudolf Haag


We show how in gravitational collapse the Hawking radiation at large times is precisely related to a scaling limit on the sphere where the star radius crosses the Schwarzschild radius (as long as the back reaction of the radiation on the metric is neglected). For a free quantum field it can be exactly evaluated and the result agrees with Hawking's prediction. For a realistic quantum field theory no evaluation based on general principles seems possible. The outcoming radiation depends on the field theoretical model.


Radiation Neural Network Black Hole Statistical Physic Field Theory 
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  1. 1.
    Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time, Cambridge: Cambridge University Press 1980Google Scholar
  2. 2.
    Bekenstein, J.D.: Phys. Rev.D7, 2333 (1973)CrossRefGoogle Scholar
  3. 3.
    Hawking, S.W.: Commun. Math. Phys.43, 199 (1975)Google Scholar
  4. 4.
    Bisognano, J.J. Wichmann, E.H.: J. Math. Phys.17, 303 (1976)CrossRefGoogle Scholar
  5. 5.
    Sewell, G.L.: Phys. Lett.79A, 23 (1980)Google Scholar
  6. 6.
    Unruh, W.G.: Phys. Rev.D14, 870 (1976)CrossRefGoogle Scholar
  7. 7.
    Fulling, S.A.: Phys. Rev.D7, 2850 (1973)CrossRefGoogle Scholar
  8. 8.
    Haag, R., Narnhofer, H., Stein, U.: Commun. Math. Phys.94, 219 (1984)CrossRefGoogle Scholar
  9. 9.
    Fredenhagen, K., Haag, R.: Commun. Math. Phys.108, 91 (1987)CrossRefGoogle Scholar
  10. 10.
    Adler, S., Liebermann, J., Ng, Y.J.: Ann. Phys.106, 279 (1978); Adler, S., Liebermann, J.: Ann. Phys.113, 294 (1977)Google Scholar
  11. 11.
    Wald, R.M.: Commun. Math. Phys.54, 1 (1977); Phys. Rev.D17, 1477 (1978)CrossRefGoogle Scholar
  12. 12.
    Fulling, S.A., Sweeny, M., Wald, R.M.: Commun. Math. Phys.63, 257 (1981)CrossRefGoogle Scholar
  13. 13.
    Fulling, S.A., Narcowich, F.J., Wald, R.M.: Ann. Phys. (N.Y.)136, 243 (1981)CrossRefGoogle Scholar
  14. 14.
    Kay, B.S., Wald, R.M.: Proceedings of the XVth international conference on differential geometric methods in theoretical physics (Clausthal 1986) Doebner, H.D., Henning, J.D. (eds.). Singapore: World Scientific 1987; Kay, B.S., Wald, R.M.: Theorems on the uniqueness and thermal properties of stationary, nonsingular, quasi-free states on spacetime with a bifurcate killing horizon (Preprint 1988)Google Scholar
  15. 15.
    Bernard, D.: Phys. Rev.D33, 3581 (1986)CrossRefGoogle Scholar
  16. 16.
    Hartle, J.R., Hawking, S.W.: Phys. Rev.D13, 2188 (1976)CrossRefGoogle Scholar
  17. 17.
    Gibbons, E.W., Hawking, S.W.: Phys. Rev.D15, 2738 (1977)CrossRefGoogle Scholar
  18. 18.
    Dimock, J., Kay, B.S.: Ann. Phys. (N.Y.)175, 366 (1987)CrossRefGoogle Scholar
  19. 19.
    De Alfaro, V., Regge, T.: Potential scattering. Amsterdam: North-Holland 1965Google Scholar

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Klaus Fredenhagen
    • 1
  • Rudolf Haag
    • 2
  1. 1.Institut für Theorie der ElementarteilchenFU BerlinW. BerlinFederal Republic of Germany
  2. 2.II. Institut für Theoretische PhysikUniversität HamburgHamburgFederal Republic of Germany

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