Particle creation by black holes
- 11k Downloads
- 5.4k Citations
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.
Keywords
Entropy Neural Network Black Hole Nonlinear Dynamics Classical TheoryPreview
Unable to display preview. Download preview PDF.
References
- 1.Isham, C.J.: Preprint (1973)Google Scholar
- 2.Ashtekar, A., Geroch, R.P.: Quantum theory of gravity (preprint 1973)Google Scholar
- 3.Penrose, R.: Phys. Rev. Lett.14, 57–59 (1965)CrossRefADSMATHMathSciNetGoogle Scholar
- 4.Hawking, S.W.: Proc. Roy. Soc. Lond.A 300, 187–20 (1967)ADSMATHGoogle Scholar
- 5.Hawking, S.W., Penrose, R.: Proc. Roy. Soc. Lond.A 314, 529–548 (1970)ADSMathSciNetGoogle Scholar
- 6.Hawking, S.W., Ellis, G.F.R.: The large scale structure of space-time. London: Cambridge University Press 1973Google Scholar
- 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.Bardeen, J.M., Carter, B., Hawking, S.W.: Commun. math. Phys.31, 161–170 (1973)CrossRefMathSciNetGoogle Scholar
- 9.Hawking, S.W.: Mon, Not. Roy. astr. Soc.152, 75–78 (1971)ADSGoogle Scholar
- 10.Carr, B.J., Hawking, S.W.: Monthly Notices Roy. Astron. Soc.168, 399–415 (1974)ADSGoogle Scholar
- 11.Hagedorn, R.: Astron. Astrophys.5, 184 (1970)ADSMATHGoogle Scholar
- 12.Hawking, S.W.: Commun. math. Phys.25, 152–166 (1972)MathSciNetGoogle Scholar
- 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.Misner, C.W.: Bull. Amer. Phys. Soc.17, 472 (1972)Google Scholar
- 15.Press, W.M., Teukolsky, S.A.: Nature238, 211 (1972)CrossRefADSGoogle 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 1965Google Scholar
- 19.Beckenstein, J.D.: Phys. Rev. D.7, 2333–2346 (1973)ADSMathSciNetGoogle Scholar
- 20.Beckenstein, J.D.: Phys. Rev. D.9,Google Scholar
- 21.Penrose, R.: Phys. Rev. Lett.10, 66–68 (1963)CrossRefADSMathSciNetGoogle Scholar
- 22.Sachs, R.K.: Proc. Roy. Soc. Lond.A 270, 103 (1962)ADSMATHMathSciNetGoogle Scholar
- 23.Eardley, D., Sachs, R.K.: J. Math. Phys.14 (1973)Google Scholar
- 24.Schmidt, B.G.: Commun. Math. Phys.36, 73–90 (1974)CrossRefMATHGoogle Scholar
- 25.Bondi, H., van der Burg, M.G.J., Metzner, A.W.K.: Proc. Roy. Soc. Lond.A 269, 21 (1962)ADSGoogle Scholar
- 26.Carter, B.: Commun. math. Phys.10, 280–310 (1968)MATHMathSciNetGoogle Scholar
- 27.Teukolsky, S.A.: Ap. J.185, 635–647 (1973)CrossRefADSGoogle Scholar
- 28.Unruh, W.: Phys. Rev. Lett.31, 1265 (1973)CrossRefADSGoogle Scholar
- 29.Unruh, W.: Phys. Rev. D.10, 3194–3205 (1974)CrossRefADSGoogle Scholar
- 30.Zeldovich, Ya.B., Starobinsky, A.A.: Zh. E.T.F.61, 2161 (1971), JETP34, 1159 (1972)Google Scholar