Communications in Mathematical Physics

, Volume 43, Issue 3, pp 199–220 | Cite as

Particle creation by black holes

  • S. W. Hawking


In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.


Entropy Neural Network Black Hole Nonlinear Dynamics Classical Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Isham, C.J.: Preprint (1973)Google Scholar
  2. 2.
    Ashtekar, A., Geroch, R.P.: Quantum theory of gravity (preprint 1973)Google Scholar
  3. 3.
    Penrose, R.: Phys. Rev. Lett.14, 57–59 (1965)CrossRefADSzbMATHMathSciNetGoogle Scholar
  4. 4.
    Hawking, S.W.: Proc. Roy. Soc. Lond.A 300, 187–20 (1967)ADSzbMATHGoogle Scholar
  5. 5.
    Hawking, S.W., Penrose, R.: Proc. Roy. Soc. Lond.A 314, 529–548 (1970)ADSMathSciNetGoogle Scholar
  6. 6.
    Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. London: Cambridge University Press 1973Google Scholar
  7. 7.
    Hawking, S.W.: The event horizon. In: Black holes. Ed. C.M. DeWitt, B.S. DeWitt. New York: Gordon and Breach 1973Google Scholar
  8. 8.
    Bardeen, J.M., Carter, B., Hawking, S.W.: Commun. math. Phys.31, 161–170 (1973)CrossRefMathSciNetGoogle Scholar
  9. 9.
    Hawking, S.W.: Mon, Not. Roy. astr. Soc.152, 75–78 (1971)ADSGoogle Scholar
  10. 10.
    Carr, B.J., Hawking, S.W.: Monthly Notices Roy. Astron. Soc.168, 399–415 (1974)ADSGoogle Scholar
  11. 11.
    Hagedorn, R.: Astron. Astrophys.5, 184 (1970)ADSzbMATHGoogle Scholar
  12. 12.
    Hawking, S.W.: Commun. math. Phys.25, 152–166 (1972)MathSciNetGoogle Scholar
  13. 13.
    Carter, B.: Black hole equilibrium states. In: Black holes. Ed. C.M. DeWitt, B.S. DeWitt. New York: Gordon and Breach 1973Google Scholar
  14. 14.
    Misner, C.W.: Bull. Amer. Phys. Soc.17, 472 (1972)Google Scholar
  15. 15.
    Press, W.M., Teukolsky, S.A.: Nature238, 211 (1972)CrossRefADSGoogle Scholar
  16. 16.
    Starobinsky, A.A.: Zh.E.T.F.64, 48 (1973)Google Scholar
  17. 17.
    Starobinsky, A.A., Churilov, S.M.: Zh.E.T.F.65, 3 (1973)Google Scholar
  18. 18.
    Bjorken, T.D., Drell, S.D.: Relativistic quantum mechanics. New York: McGraw Hill 1965Google Scholar
  19. 19.
    Beckenstein, J.D.: Phys. Rev. D.7, 2333–2346 (1973)ADSMathSciNetGoogle Scholar
  20. 20.
    Beckenstein, J.D.: Phys. Rev. D.9,Google Scholar
  21. 21.
    Penrose, R.: Phys. Rev. Lett.10, 66–68 (1963)CrossRefADSMathSciNetGoogle Scholar
  22. 22.
    Sachs, R.K.: Proc. Roy. Soc. Lond.A 270, 103 (1962)ADSzbMATHMathSciNetGoogle Scholar
  23. 23.
    Eardley, D., Sachs, R.K.: J. Math. Phys.14 (1973)Google Scholar
  24. 24.
    Schmidt, B.G.: Commun. Math. Phys.36, 73–90 (1974)CrossRefzbMATHGoogle Scholar
  25. 25.
    Bondi, H., van der Burg, M.G.J., Metzner, A.W.K.: Proc. Roy. Soc. Lond.A 269, 21 (1962)ADSGoogle Scholar
  26. 26.
    Carter, B.: Commun. math. Phys.10, 280–310 (1968)zbMATHMathSciNetGoogle Scholar
  27. 27.
    Teukolsky, S.A.: Ap. J.185, 635–647 (1973)CrossRefADSGoogle Scholar
  28. 28.
    Unruh, W.: Phys. Rev. Lett.31, 1265 (1973)CrossRefADSGoogle Scholar
  29. 29.
    Unruh, W.: Phys. Rev. D.10, 3194–3205 (1974)CrossRefADSGoogle Scholar
  30. 30.
    Zeldovich, Ya.B., Starobinsky, A.A.: Zh. E.T.F.61, 2161 (1971), JETP34, 1159 (1972)Google Scholar

Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • S. W. Hawking
    • 1
    • 2
  1. 1.Department of Applied Mathematics and Theoretical PhysicsUniversity of CambridgeCambridgeEngland
  2. 2.California Institute of TechnologyPasadenaUSA

Personalised recommendations