On the Local Existence for the Characteristic Initial Value Problem in General Relativity

2011/07/05 by Jonathan Luk, Luk, Jonathan · 5 citations
Mathematics · Physics and Astronomy · #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Mathematical Physics (math-ph) #Relativity and Gravitational Theory #gr-qc #math-ph #math.AP #math.MP

paper · pdf · doi:10.48550/arxiv.1107.0898

arxiv created 2011/07/05 · openalex publication_date 2011/07/05 · arxiv updated 2011/07/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Given a truncated incoming null cone and a truncated outgoing null cone intersecting at a two sphere S with smooth characteristic initial data, a theorem of Rendall shows that the vacuum Einstein equations can be solved in a small neighborhood of S in the future of S. We show that in fact the vacuum Einstein equations can be solved in a neighborhood in the future of the cones, as long as the constraint equations are initially satisfied on the null cones. The proof is based on energy type estimates and relies heavily on the null structure of the Einstein equations in the double null foliation.

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• Controlled regularity at future null infinity from past asymptotic initial data: the wave equation

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