General Relativity and Gravitation

, Volume 27, Issue 10, pp 1017–1021 | Cite as

Are all static black hole solutions spherically symmetric?

  • S. Alexander Ridgway
  • Erick J. Weinberg


The static black hole solutions to the Einstein-Maxwell equations are all spherically symmetric, as are many of the recently discovered black hole solutions in theories of gravity coupled to other forms of matter. However, counterexamples demonstrating that static black holes need not be spherically symmetric exist in theories, such as the standard electroweak model, with electrically charged massive vector fields. In such theories, a magnetically charged Reissner-Nordström solution with sufficiently small horizon radius is unstable against the development of a nonzero vector field outside the horizon. General arguments show that, for generic values of the magnetic charge, this field cannot be spherically symmetric. Explicit construction of the solution shows that it in fact has no rotational symmetry at all.


Black Hole Vector Field Differential Geometry Black Hole Solution Rotational Symmetry 
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Copyright information

© Plenum Publishing Corporation 1995

Authors and Affiliations

  • S. Alexander Ridgway
    • 1
  • Erick J. Weinberg
    • 1
  1. 1.Physics DepartmentColumbia UniversityNew YorkUSA

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