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Black Holes: Scatterers, Absorbers and Emitters of Particles

  • N. Sanchez
Chapter
Part of the NATO Science Series book series (NAII, volume 40)

Abstract

Accurate and powerful computational methods developped by the author, based on the analytic resolution of the wave equation in the black hole background, allow to obtain the highly non trivial total absorption spectrum of the Black Hole. As well as phase shifts and cross sections (elastic and inelastic) for a wide range of energy and angular momentum, the angular distribution of absorbed and scattered waves, and the Hawking emission rates. The total absorption spectrum of waves by the Black Hole is known exactly. It presents as a function of frequency a remarkable oscillatory behaviour characteristic of a diffraction pattern. It oscillates around its optical geometric limit \( \left( {\tfrac{{27}} {4}\pi r_s ^2 } \right) \) with decreasing amplitude and almost constant period. This is an unique distinctive feature of the black hole absorption, and due to its r = 0 singularity. Ordinary absorptive bodies and optical models do not present these features.

The Hamiltonian describing the wave-black hole interaction is non hermitian (despite being real) due to its singularity at the origin (r = 0). The unitarity optical theorem of scattering theory is generalized to the black hole case explicitely showing that absorption takes place only at the origin (r = 0).

All these results allow to understand and reproduce the Black Hole absorption spectrum in terms of Fresnel-Kirchoff diffraction theory: interference takes place between the absorbed rays arriving at the origin by different optical paths.

These fundamental features of the Black Hole Absorption will be present for generic higher dimensional Black Hole backgrounds, and whatever the low energy effective theory they arise from.

In recent and increasing litterature devoted to compute absorption cross sections (“grey body factors”) of black holes (whatever ordinary, stringy, D-braned), the fundamental remarkable features of the Black Hole Absorption spectrum are overlooked.

Keywords

Black Hole Angular Momentum Phase Shift Partial Wave Absorption Cross Section 
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.

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References

  1. [1]
    S. Hawking, “Particle Creation by Black Holes”, Comm. Math. Phys. 43 (1975) 199.MathSciNetADSCrossRefGoogle Scholar
  2. [2]
    N. Sánchez, “Absorption and Emission Spectra for a Schwarzschild Black Hole“, Phys.Rev. D18 (1978) 1030.ADSGoogle Scholar
  3. [3]
    N. Sánchez, “Wave Scattering Theory and the Absorption Problem for a Black Hole”, Phys.Rev. D16 (1977) 937.ADSGoogle Scholar
  4. [4]
    N. Sánchez, “Elastic Scattering of Waves by a Black Hole”, Phys.Rev. D18 (1978) 1798.ADSGoogle Scholar
  5. [5]
    N. Sánchez, “Scattering of Scalar Waves from a Schwarzschild Black Hole”, J.Math.Phys. 17 (1976) 688.ADSCrossRefGoogle Scholar
  6. [6]
    N. Sánchez, “Sur la Physique des Champs et la Géométrie de l’Espace-Temps”, Thèse d’Etat, Paris (1979).Google Scholar
  7. [7]
    J.A.H. Futterman, F.A.Handler and R.A.Matzner, “Scattering from Black Holes”, Cambridge University Press, Cambridge, U.K. (1988), and references therein.MATHCrossRefGoogle Scholar
  8. [8]
    S. Persides, Int.Jour.Math.Phys. 48 (1976) 165; 50 (1976) 229.MathSciNetADSMATHGoogle Scholar
  9. [9]
    A.A. Starobinsky, Zh.Eks.Teor.Fiz. 64 (1973) 48. (Sov.Phys.-JETP 37(1973)1).ADSGoogle Scholar
  10. [10]
    W.G. Unruh, Phys.Rev. D14 (1976) 3251.ADSGoogle Scholar
  11. [11]
    For example: S.S. Gubser and I.R. Klebanov, Phys.Rev.Lett. 77 (1996) 4491; J.Maldacena and A.Strominger, Phys.Rev.D55 (1997) 861 and Phys.Rev.D56 (1997) 4975; S.S.Gubser, Phys.Rev.D56 (1997) 4984 and hep-th/9706100; M.Civetič and F.Larsen, Phys.Rev.D56 (1997) 4994 and hep-th/9705192; I.R.Klebanov and S.D.Mathur, hep-th/9701187; S.Das, A.Dasgupta and T.Sarkar, Phys.Rev.D55 (1997) 12; S.P. de Alwis and K.Sato, Phys.Rev.D55 (1997) 6181; R.Emparan, hep-th/9704204; H.W.Lee, Y.S.Myung and J.Y.Kim, hep-th/9708099.MathSciNetADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2001

Authors and Affiliations

  • N. Sanchez
    • 1
  1. 1.Observatoire de Paris-DEMIRM/LERMAParisFrance

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