Abstract
We prove existence of vacuum space-times with freely prescribable cone-smooth initial data on past null infinity.
Highlights
In order to present our result some terminology and notation is needed: Let CO denote the light-cone of the origin O in Minkowski space-time
We prove the following: Theorem 1.1 Let CO be the light-cone of the origin O in Minkowski spacetime
The task consists of constructing initial data, for those equations, which arise as the restriction to the future light-cone I − of past timelike infinity i− of tensors which are smooth in the unphysical space-time
Summary
In order to present our result some terminology and notation is needed: Let CO denote the (future) light-cone of the origin O in Minkowski space-time (throughout this work, by “light-cone of a point O” we mean the subset of a spacetime M covered by future directed null geodesics issued from O). There exist smooth fields (gμν, Lμν, Cμνσρ, Θ, s) defined in a neighbourhood of i− such that the fields (gμν , Lμν , dμνσρ = Θ−1Cμνσ ρ, Θ, s) solve the conformal field equations (2.1)-(2.6) in I+(i−), satisfy the gauge conditions (2.17), with
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