Extremal Isolated Horizons: A Local Uniqueness Theorem

Abstract

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.

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

References in corpus (3)

• Mechanics of Rotating Isolated Horizons
• Geometry of Generic Isolated Horizons
• Geometric Characterizations of the Kerr Isolated Horizon

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