Global characteristic problem for Einstein vacuum equations with small initial data: (I) The initial data constraints

2004/09/06 by Giulio Caciotta, Caciotta, Giulio, F. Nicolò +2
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Navier-Stokes equation solutions #gr-qc

paper · pdf · doi:10.48550/arxiv.gr-qc/0409028

77 pages, no figures; corrected misprints and minor errors, to appear on Journal of Hyperbolic Differential Equations (JHDE)

arxiv created 2004/10/13 · arxiv updated 2009/12/01

Abstract

We show how to prescribe the initial data of a characteristic problem satisfying the costraints, the smallness, the regularity and the asymptotic decay suitable to prove a global existence result. In this paper, the first of two, we show in detail the construction of the initial data and give a sketch of the existence result. This proof, which mimicks the analogous one for the non characteristic problem in [Kl-Ni], will be the content of a subsequent paper.

Citations

• Uniform decay estimates and the lorentz invariance of the classical wave equation

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