Extremal Isolated Horizons: A Local Uniqueness Theorem

Details Extremal Isolated Horizons: A Local Uniqueness Theorem Extremal Isolated Horizons: A Local Uniqueness Theorem

2002-08-13

arxiv.org/abs/gr-qc/0208032v3

Class.Quant.Grav. 20 (2003) 587-606

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

22 pages, page size changed, typos and equations (142), (143a) corrected, PACS number added

Scientific paper

We derive all the axi-symmetric, vacuum and electrovac extremal isolated horizons. It turns out that for every horizon in this class, the induced metric tensor, the rotation 1-form potential and the pullback of the electromagnetic field necessarily coincide with those induced by the monopolar, extremal Kerr-Newman solution on the event horizon. We also discuss the general case of a symmetric, extremal isolated horizon. In particular, we analyze the case of a two-dimensional symmetry group generated by two null vector fields. Its relevance to the classification of all the symmetric isolated horizons, including the non-extremal once, is explained.

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