On Hawking's Local Rigidity Theorems for Charged Black Holes

Abstract

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, Rácz 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.

20 pages

References in corpus (3)

• On the Rigidity Theorem for Spacetimes with a Stationary Event Horizon or a Compact Cauchy Horizon
• On the uniqueness of smooth, stationary black holes in vacuum
• Uniqueness results for ill posed characteristic problems in curved space-times

Cited by in corpus (2)

• Stationary Black Holes: Uniqueness and Beyond
• On the local extension of Killing vector fields in electrovacuum spacetimes