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

2011/07/05 by Jonathan Luk, Luk, Jonathan · 5 citations
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

paper · pdf · doi:10.48550/arxiv.1107.0898

openalex publication_date 2011/07/05 · 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\nintersecting at a two sphere S with smooth characteristic initial data, a\ntheorem of Rendall shows that the vacuum Einstein equations can be solved in a\nsmall neighborhood of S in the future of S. We show that in fact the vacuum\nEinstein equations can be solved in a neighborhood in the future of the cones,\nas long as the constraint equations are initially satisfied on the null cones.\nThe proof is based on energy type estimates and relies heavily on the null\nstructure of the Einstein equations in the double null foliation.\n

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• On the local existence for the characteristic initial value problem for the Einstein-Dirac system
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• Controlled regularity at future null infinity from past asymptotic initial data: the wave equation

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