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Particle creation by black holes

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Abstract

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.

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ArticleOpen access24 April 2021

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References

  1. Isham, C.J.: Preprint (1973)

  2. Ashtekar, A., Geroch, R.P.: Quantum theory of gravity (preprint 1973)

  3. Penrose, R.: Phys. Rev. Lett.14, 57–59 (1965)

    Article ADS MATH MathSciNet  Google Scholar 

  4. Hawking, S.W.: Proc. Roy. Soc. Lond.A 300, 187–20 (1967)

    ADS MATH  Google Scholar 

  5. Hawking, S.W., Penrose, R.: Proc. Roy. Soc. Lond.A 314, 529–548 (1970)

    ADS MathSciNet  Google Scholar 

  6. Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. London: Cambridge University Press 1973

    Google Scholar 

  7. Hawking, S.W.: The event horizon. In: Black holes. Ed. C.M. DeWitt, B.S. DeWitt. New York: Gordon and Breach 1973

    Google Scholar 

  8. Bardeen, J.M., Carter, B., Hawking, S.W.: Commun. math. Phys.31, 161–170 (1973)

    Article MathSciNet  Google Scholar 

  9. Hawking, S.W.: Mon, Not. Roy. astr. Soc.152, 75–78 (1971)

    ADS  Google Scholar 

  10. Carr, B.J., Hawking, S.W.: Monthly Notices Roy. Astron. Soc.168, 399–415 (1974)

    ADS  Google Scholar 

  11. Hagedorn, R.: Astron. Astrophys.5, 184 (1970)

    ADS MATH  Google Scholar 

  12. Hawking, S.W.: Commun. math. Phys.25, 152–166 (1972)

    MathSciNet  Google Scholar 

  13. Carter, B.: Black hole equilibrium states. In: Black holes. Ed. C.M. DeWitt, B.S. DeWitt. New York: Gordon and Breach 1973

    Google Scholar 

  14. Misner, C.W.: Bull. Amer. Phys. Soc.17, 472 (1972)

    Google Scholar 

  15. Press, W.M., Teukolsky, S.A.: Nature238, 211 (1972)

    Article ADS  Google Scholar 

  16. Starobinsky, A.A.: Zh.E.T.F.64, 48 (1973)

    Google Scholar 

  17. Starobinsky, A.A., Churilov, S.M.: Zh.E.T.F.65, 3 (1973)

    Google Scholar 

  18. Bjorken, T.D., Drell, S.D.: Relativistic quantum mechanics. New York: McGraw Hill 1965

    Google Scholar 

  19. Beckenstein, J.D.: Phys. Rev. D.7, 2333–2346 (1973)

    ADS MathSciNet  Google Scholar 

  20. Beckenstein, J.D.: Phys. Rev. D.9,

  21. Penrose, R.: Phys. Rev. Lett.10, 66–68 (1963)

    Article ADS MathSciNet  Google Scholar 

  22. Sachs, R.K.: Proc. Roy. Soc. Lond.A 270, 103 (1962)

    ADS MATH MathSciNet  Google Scholar 

  23. Eardley, D., Sachs, R.K.: J. Math. Phys.14 (1973)

  24. Schmidt, B.G.: Commun. Math. Phys.36, 73–90 (1974)

    Article MATH  Google Scholar 

  25. Bondi, H., van der Burg, M.G.J., Metzner, A.W.K.: Proc. Roy. Soc. Lond.A 269, 21 (1962)

    ADS  Google Scholar 

  26. Carter, B.: Commun. math. Phys.10, 280–310 (1968)

    MATH MathSciNet  Google Scholar 

  27. Teukolsky, S.A.: Ap. J.185, 635–647 (1973)

    Article ADS  Google Scholar 

  28. Unruh, W.: Phys. Rev. Lett.31, 1265 (1973)

    Article ADS  Google Scholar 

  29. Unruh, W.: Phys. Rev. D.10, 3194–3205 (1974)

    Article ADS  Google Scholar 

  30. Zeldovich, Ya.B., Starobinsky, A.A.: Zh. E.T.F.61, 2161 (1971), JETP34, 1159 (1972)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge, England

    S. W. Hawking

  2. California Institute of Technology, W. K. Kellogg Radiation Lab. 106–38, 91125, Pasadena, California, USA

    S. W. Hawking

Authors
  1. S. W. Hawking

Additional information

Communicated by J. Ehlers

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