Astrophysics and Space Science

, Volume 266, Issue 3, pp 371–378 | Cite as

Relativistic Rotational Darkening of Lightlike Radiation and Von Zeipel's Theorem for Radially Emitting Spheroids

  • Andreas de Vries
  • Theodor Schmidt-Kaler


It is shown that an outgoing null radiation field in the outer space of a Kerr-Newman black hole is darkened by the rotation of the black hole. This rotational darkening is calculated for a spheroid emitting null radiation normally to its surface, yielding the von Zeipel-like effectthat the equatorial region is darkened more strongly than the polar regions.This effect is not confined to the case of black holes but is also observable for relativistically rotating fluid spheroids such as atmospheres of pulsars or neutron stars. Moreover, application to Hawking radiation suggests that the black hole cannot be viewed as a classical black body but that the Hawking radiationis a global geometric effect.


Black Hole Neutron Star Event Horizon Equatorial Plane Outer Space 
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  1. Carter, B.: 1968, Phys. Rev. 174,5, 1559.zbMATHCrossRefADSGoogle Scholar
  2. Chandrasekhar, S.: 1983, The Mathematical Theory of Black Holes, Oxford University Press, Oxford.Google Scholar
  3. Cunningham, C. T.: 1975, Astrophys. J. 202, 788.CrossRefADSGoogle Scholar
  4. de Vries, A.: 1994, Über die Beschränktheit der Energienorm bei der Evolution der Dirac, Weylund Maxwellfelder in gekrümmten Raumzeiten, Brockmeyer, BochumGoogle Scholar
  5. de Vries, A.: 1995, Manuscripta Math. 88, 233.zbMATHMathSciNetGoogle Scholar
  6. de Vries, A.: 1996, Math. Nachr. 179, 27.zbMATHMathSciNetGoogle Scholar
  7. de Vries, A., Schmidt-Kaler, T. and Böhme, R.: 1995, Astrophys. Space Sci. 225, 221.zbMATHCrossRefADSGoogle Scholar
  8. Hawking, S.W.: 1975, Commun. Math. Phys. 43, 199.MathSciNetCrossRefGoogle Scholar
  9. Hawking, S.W.: 1976, Phys. Rev. D 13,2, 191.ADSGoogle Scholar
  10. Kojima, Y.: 1991, Mon. Not. R. Astron. Soc. 250, 629.ADSGoogle Scholar
  11. P.T. Landsberg: 1992, in: V. De Sabbata and Zh. Zhang (eds.), Black Hole Physics, Kluwer Academic Publishers, Dordrecht.Google Scholar
  12. Sexl, R.U. and Urbantke, H.K.: 1987, Gravitation und Kosmologie, BI Wissenschaftsverlag, Mannheim.Google Scholar
  13. Tassoul, J.-L.: 1978, Theory of Rotating Stars, Princeton University Press, Princeton, New Jersey.Google Scholar
  14. Walker, M. and Penrose, R.: 1970, Commun. Math. Phys. 18, 265.zbMATHMathSciNetCrossRefADSGoogle Scholar
  15. von Zeipel, H.: 1924, Mon. Not. R. Astron. Soc. London 84, 665.ADSGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1999

Authors and Affiliations

  • Andreas de Vries
    • 1
  • Theodor Schmidt-Kaler
    • 2
  1. 1.Institut für Mathematik der Ruhr-UniversitätBochumGermany; E-mail
  2. 2.Astronomisches Institut der Ruhr-UniversitätBochumGermany (Georg-Büchner-Straße 37, D-97276 Margetshöchheim, Germany)

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