Skip to main content
SpringerLink
Log in

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

  • Published:
Communications in Mathematical Physics Aims and scope Submit manuscript

Abstract

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time, Cambridge: Cambridge University Press 1980

    Google Scholar 

  2. Bekenstein, J.D.: Phys. Rev.D7, 2333 (1973)

    Article  Google Scholar 

  3. Hawking, S.W.: Commun. Math. Phys.43, 199 (1975)

    Google Scholar 

  4. Bisognano, J.J. Wichmann, E.H.: J. Math. Phys.17, 303 (1976)

    Article  Google Scholar 

  5. Sewell, G.L.: Phys. Lett.79A, 23 (1980)

    Google Scholar 

  6. Unruh, W.G.: Phys. Rev.D14, 870 (1976)

    Article  Google Scholar 

  7. Fulling, S.A.: Phys. Rev.D7, 2850 (1973)

    Article  Google Scholar 

  8. Haag, R., Narnhofer, H., Stein, U.: Commun. Math. Phys.94, 219 (1984)

    Article  Google Scholar 

  9. Fredenhagen, K., Haag, R.: Commun. Math. Phys.108, 91 (1987)

    Article  Google Scholar 

  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. Wald, R.M.: Commun. Math. Phys.54, 1 (1977); Phys. Rev.D17, 1477 (1978)

    Article  Google Scholar 

  12. Fulling, S.A., Sweeny, M., Wald, R.M.: Commun. Math. Phys.63, 257 (1981)

    Article  Google Scholar 

  13. Fulling, S.A., Narcowich, F.J., Wald, R.M.: Ann. Phys. (N.Y.)136, 243 (1981)

    Article  Google Scholar 

  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. Bernard, D.: Phys. Rev.D33, 3581 (1986)

    Article  Google Scholar 

  16. Hartle, J.R., Hawking, S.W.: Phys. Rev.D13, 2188 (1976)

    Article  Google Scholar 

  17. Gibbons, E.W., Hawking, S.W.: Phys. Rev.D15, 2738 (1977)

    Article  Google Scholar 

  18. Dimock, J., Kay, B.S.: Ann. Phys. (N.Y.)175, 366 (1987)

    Article  Google Scholar 

  19. De Alfaro, V., Regge, T.: Potential scattering. Amsterdam: North-Holland 1965

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theorie der Elementarteilchen, FU Berlin, W. Berlin, Federal Republic of Germany

    Klaus Fredenhagen

  2. II. Institut für Theoretische Physik, Universität Hamburg, Hamburg, Federal Republic of Germany

    Rudolf Haag

Authors
  1. Klaus Fredenhagen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rudolf Haag
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by A. Jaffe

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fredenhagen, K., Haag, R. On the derivation of Hawking radiation associated with the formation of a black hole. Commun.Math. Phys. 127, 273–284 (1990). https://doi.org/10.1007/BF02096757

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02096757

Keywords

Search

Navigation