Annales Henri Poincaré

, Volume 16, Issue 7, pp 1551–1581 | Cite as

On Perturbations of Extreme Kerr–Newman Black Holes and their Evolution

  • Martin ReirisEmail author


Using black hole inequalities and the increase of the horizon’s areas, we show that there are arbitrarily small electro-vacuum perturbations of the standard initial data of the extreme Reissner–Nordström black hole that (by contradiction) cannot decay in time into any extreme Kerr–Newman black hole. This proves that, in a formal sense, the reduced family of the extreme Kerr–Newman black holes is unstable. It remains of course to be seen whether the whole family of charged black holes, including those extremes, is stable or not.


Black Hole Event Horizon Conformal Factor Extreme Black Hole Cauchy Horizon 
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.


  1. 1.
    Aretakis, S.: Horizon instability of extremal black holes (2012) arXiv:1206.6598
  2. 2.
    Aronszajn N.: A unique continuation theorem for solutions of elliptic partial differential equations or inequalities of second order. J. Math. Pures Appl. (9) 36, 235–249 (1957)zbMATHMathSciNetGoogle Scholar
  3. 3.
    Bizon P., Friedrich H.: A remark about wave equations on the extreme Reissner–Nordstróm black hole exterior. Class. Quant. Grav. 30, 065001 (2013)MathSciNetADSCrossRefGoogle Scholar
  4. 4.
    Camacho C., Lins Neto A.: Geometric Theory of Foliations. Birkhäuser Boston Inc., Boston (1985)zbMATHCrossRefGoogle Scholar
  5. 5.
    Carter, B.: Black hole equilibrium states. In: Black holes/Les astres occlus (École d’Été Phys. Théor. Les Houches, 1972), pp. 57–214. Gordon and Breach, New York (1973)Google Scholar
  6. 6.
    Choquet-Bruhat, Y., York, J.W. Jr.: The Cauchy problem. In: General Relativity and Gravitation, vol. 1, pp. 99–172. Plenum, New York (1980)Google Scholar
  7. 7.
    Chrusciel P.T., Delay E., Galloway G.J., Howard R.: The Area theorem. Annales Henri Poincaré 2, 109–178 (2001)zbMATHMathSciNetADSCrossRefGoogle Scholar
  8. 8.
    Chrusciel, P.T., Mazzeo, R.: Initial data sets with ends of cylindrical type: I. The Lichnerowicz Equation. arXiv:1201.4937
  9. 9.
    Colding, T.H., Minicozzi, W.P. II.: A course in minimal surfaces. In: Graduate Studies in Mathematics, vol. 121. American Mathematical Society, Providence, RI (2011)Google Scholar
  10. 10.
    Dain S.: Geometric inequalities for axially symmetric black holes. Class. Quant. Grav. 29, 073001 (2012)MathSciNetADSCrossRefGoogle Scholar
  11. 11.
    Dain S., Dotti G.: The wave equation on the extreme Reissner–Nordstróm black hole. Class. Quant. Grav. 30, 055011 (2013)MathSciNetADSCrossRefGoogle Scholar
  12. 12.
    Dain S., Jaramillo J.L., Reiris M.: Area-charge inequality for black holes. Class. Quant. Grav. 29, 035013 (2012)MathSciNetADSCrossRefGoogle Scholar
  13. 13.
    Figueras P., Murata K., Reall H.S.: Black hole instabilities and local Penrose inequalities. Class. Quant. Grav. 28, 225030 (2011)MathSciNetADSCrossRefGoogle Scholar
  14. 14.
    Lucietti J., Murata K., Reall H.S., Tanahashi N.: On the horizon instability of an extreme Reissner–Nordstróm black hole. JHEP 1303, 035 (2013)MathSciNetADSCrossRefGoogle Scholar
  15. 15.
    Lucietti J., Reall H.S.: Gravitational instability of an extreme Kerr black hole. Phys. Rev. D 86, 104030 (2012)ADSCrossRefGoogle Scholar
  16. 16.
    Meeks W. III, Simon L., Yau S.T.: Embedded minimal surfaces, exotic spheres, and manifolds with positive Ricci curvature. Ann. Math. (2) 116(3), 621–659 (1982)zbMATHMathSciNetCrossRefGoogle Scholar
  17. 17.
    Murata K., Reall H.S., Tanahashi N.: What happens at the horizon(s) of an extreme black hole? Class. Quant. Grav. 30, 235007 (2013)MathSciNetADSCrossRefGoogle Scholar
  18. 18.
    Nakauchi N.: Compactness of the space of incompressible stable minimal surfaces without boundary. J. Math. Kyoto Univ. 30(2), 343–346 (1990)zbMATHMathSciNetGoogle Scholar
  19. 19.
    Reiris M.: On extreme Kerr-throats and zero temperature black-holes. Class. Quant. Grav. 31, 025001 (2014)MathSciNetADSCrossRefGoogle Scholar
  20. 20.
    Simon, L.: Lectures on geometric measure theory. In: Proceedings of the Centre for Mathematical Analysis, Australian National University, vol. 3. Australian National University Centre for Mathematical Analysis, Canberra (1983)Google Scholar
  21. 21.
    Wald R.M.: General Relativity. University of Chicago Press, Chicago (1984)zbMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Max Planck Institute für GravitationsphysikGolmGermany

Personalised recommendations