General Relativity and Gravitation

, Volume 37, Issue 12, pp 2145–2163 | Cite as

Black holes in which the electrostatic or scalar equation is solvable in closed form

Research Article
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Abstract

We show that the method used in the Schwarzschild black hole for finding the elementary solution of the electrostatic equation in closed form cannot extend in higher dimensions. By contrast, we prove the existence of static, spherically symmetric geometries with a non-degenerate horizon in which the static scalar equation can be solved in closed form. We give the explicit results in 6 dimensions. We determine moreover the expressions of the electrostatic potential and of the static scalar field for a point source in the extremal Reissner-Nordström black holes in higher dimensions.

Keywords

Black hole Electrostatics Scalar equation 
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References

  1. 1.
    Copson, E.T.: Proc. Roy. Soc. London A 118, 184 (1928)CrossRefADSGoogle Scholar
  2. 2.
    Copson, E.T.: Proc. Roy. Soc. Edinburgh A 80, 201 (1978)MathSciNetGoogle Scholar
  3. 3.
    Linet, B.: J. Phys. A 9, 1081 (1976)CrossRefADSMathSciNetGoogle Scholar
  4. 4.
    Léauté, B., Linet, B.: Phys. Lett. A 58, 5 (1976)CrossRefADSGoogle Scholar
  5. 5.
    Linet, B.: C. R. Acad. Sc. Paris 284, 215 (1977)MATHADSMathSciNetGoogle Scholar
  6. 6.
    Mayo, A.E.: Phys. Rev. D 60, 104044 (1999)CrossRefADSMathSciNetGoogle Scholar
  7. 7.
    Wiseman, A.G.: Phys. Rev. D 61, 084014 (2000)CrossRefADSGoogle Scholar
  8. 8.
    Myers, R.C., Perry, M.J.: Annals Phys. 172, 304 (1986)CrossRefMATHADSMathSciNetGoogle Scholar
  9. 9.
    Hanni, R.S.: Phys. Rev. D 16, 1245 (1977)CrossRefADSGoogle Scholar
  10. 10.
    Zel'nikov, A.I., Frolov, V.P.: Sov. Phys. JETP 55, 191 (1982)Google Scholar
  11. 11.
    Bičák, J., Dvořák, L.: Phys. Rev. D 22, 2933 (1980)CrossRefADSGoogle Scholar
  12. 12.
    Bekenstein, J.D., Mayo, A.E.: Phys. Rev. D 61, 024022 (2000)CrossRefADSMathSciNetGoogle Scholar
  13. 13.
    Hod, S.: Phys. Rev. D 61, 024023 (2000)CrossRefADSMathSciNetGoogle Scholar
  14. 14.
    Cai, R.-G., Myung, Y.S., Ohta, N.: Class. Quant. Gravit. 18, 5429 (2001)CrossRefMATHADSMathSciNetGoogle Scholar
  15. 15.
    Linet, B., Teyssandier, P.: Gen. Rel. Grav. 10, 313 (1979)CrossRefADSMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag 2005

Authors and Affiliations

  1. 1.Laboratoire de Mathématiques et Physique Théorique, CNRS/UMR 6083Université François RabelaisTOURSFrance

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