Hawking's local rigidity theorem without analyticity

2009/02/06 by S. Alexakis, Alexakis, S., A. D. Ionescu +3
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #gr-qc #math.AP

paper · pdf · doi:10.48550/arxiv.0902.1173

arxiv created 2009/02/06 · arxiv updated 2009/12/01

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.

Related

• The asymptotic expansion of the spacetime metric at the event horizon
• On the local extension of Killing vector-fields in Ricci flat manifolds
• On the uniqueness of Kerr-de Sitter spacetimes
• On the existence of Killing fields in smooth spacetimes with a compact Cauchy horizon
• On analyticity of static vacuum metrics at non-degenerate horizons