On Hawking's Local Rigidity Theorems for Charged Black Holes

Details On Hawking's Local Rigidity Theorems for Charged Black Holes On Hawking's Local Rigidity Theorems for Charged Black Holes

2009-03-27

arxiv.org/abs/0903.4723v1

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

20 pages

Scientific paper

We show the existence of a Hawking vector field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth Einstein-Maxwell space-time without assuming the underlying space-time is analytic. It extends one result of Friedrich, R\'{a}cz and Wald, which was limited to the interior of the black hole region. Moreover, we also show, in the presence of an additional Killing vector field $T$ which tangent to the horizon and not vanishing on the bifurcate sphere, then space-time must be locally axially symmetric without the analyticity assumption. This axial symmetry plays a fundamental role in the classification theory of stationary black holes.

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