Characteristic initial data and smoothness of Scri. I. Framework and results

Abstract

We analyze the Cauchy problem for the vacuum Einstein equations with data on a complete light-cone in an asymptotically Minkowskian space-time. We provide conditions on the free initial data which guarantee existence of global solutions of the characteristic constraint equations. We present necessary-and-sufficient conditions on characteristic initial data in $3+1$ dimensions to have no logarithmic terms in an asymptotic expansion at null infinity.

32 pages, some minor modifications

References in corpus (3)

• The Cauchy problem on a characteristic cone for the Einstein equations in arbitrary dimensions
• Conformal structures of static vacuum data
• Characteristic initial data and smoothness of Scri. II. Asymptotic expansions and construction of conformally smooth data sets

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