The characteristic problem for the Einstein vacuum equations

摘要

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 noncharacteristic problem in The Evolution Problem in General Relativity by S. Kleinerman and F. Nicolò (Birkhauser) 2002, Prog. Math. Phys., Vol. 25, will be the content of a subsequent paper.