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GLOBAL CHARACTERISTIC PROBLEM FOR EINSTEIN VACUUM EQUATIONS WITH SMALL INITIAL DATA: (I) THE INITIAL DATA CONSTRAINTS

Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133-Roma, Italy

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and

FRANCESCO NICOLÒ

Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Via della Ricerca Scientifica, 00133-Roma, Italy

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https://doi.org/10.1142/S0219891605000439Cited by:14 (Source: Crossref)

Abstract

We show how to prescribe the initial data of a characteristic problem satisfying the constraints, 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 [19], will be the content of a subsequent paper.

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