2001/09/23 by S. Klainerman, Sergiù Klainerman, Igor Rodnianski +3 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #Classical Analysis and ODEs (math.CA) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #gr-qc #math.AP #math.CA #math.DG
paper · pdf · doi:10.48550/arxiv.math/0109174
arxiv created 2001/09/23 · openalex publication_date 2001/09/23 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the second in a series of three papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. In this paper we develop the geometric analysis of the Eikinal equation for microlocalized rough Einstein metrics. This is a crucial step in the derivation of the decay estimates needed in our first paper.