THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC MAPPINGS

Details THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC MAPPINGS THE UNIQUENESS THEOREM FOR ROTATING BLACK HOLE SOLUTIONS OF SELF-GRAVITATING HARMONIC MAPPINGS

1995-03-28

arxiv.org/abs/gr-qc/9503053v1

Class.Quant.Grav.12:2021-2036,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

18 pages, latex, no figures

Scientific paper

10.1088/0264-9381/12/8/017

We consider rotating black hole configurations of self-gravitating maps from spacetime into arbitrary Riemannian manifolds. We first establish the integrability conditions for the Killing fields generating the stationary and the axisymmetric isometry (circularity theorem). Restricting ourselves to mappings with harmonic action, we subsequently prove that the only stationary and axisymmetric, asymptotically flat black hole solution with regular event horizon is the Kerr metric. Together with the uniqueness result for non-rotating configurations and the strong rigidity theorem, this establishes the uniqueness of the Kerr family amongst all stationary black hole solutions of self-gravitating harmonic mappings.

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