Hawking's local rigidity theorem without analyticity

Abstract

We prove the existence of a Hawking Killing vector-field in a full neighborhood of a local, regular, bifurcate, non-expanding horizon embedded in a smooth vacuum Einstein space-time. We do not assume analyticity of the space-time. This result will be applied in a second paper to prove a perturbative version of the uniqueness of smooth, stationary black holes in vacuum.

References in corpus (2)

• Uniqueness results for ill posed characteristic problems in curved space-times
• Unique continuation for the vacuum Einstein equations