On higher dimensional black holes with abelian isometry group

Details On higher dimensional black holes with abelian isometry group On higher dimensional black holes with abelian isometry group

2008-12-17

arxiv.org/abs/0812.3424v1

J.Math.Phys.50:052501,2009

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Scientific paper

10.1063/1.3068729

We consider (n+1)--dimensional, stationary, asymptotically flat, or Kaluza-Klein asymptotically flat black holes, with an abelian $s$--dimensional subgroup of the isometry group satisfying an orthogonal integrability condition. Under suitable regularity conditions we prove that the area of the group orbits is positive on the domain of outer communications, vanishing only on its boundary and on the "symmetry axis". We further show that the orbits of the connected component of the isometry group are timelike throughout the domain of outer communications. Those results provide a starting point for the classification of such black holes. Finally, we show non-existence of zeros of static Killing vectors on degenerate Killing horizons, as needed for the generalisation of the static no-hair theorem to higher dimensions.

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