The boost problem

We consider the vacuum Einstein equations on R4 with initial data on the hyperplane X0 = 0 which I call Σ. The initial data on Σ consists of a complete riemannian metric g and a 2-covariant symmetric tensor field k such that the pair (g,k) satisfies the initial value constraints. The local-in-time problem is to find an open set Ω contains or eqal or R4, Ω contains Σ, and on this set a Lorentz metric γ, solution to the vacuum Einstein equations in Ω, such that (g,k) are respectively the first and second fundamental forms of Σ relative to γ and (Ω, γ) is a globally hyperbolic spacetime [Σ is a Cauchy surface of (Ω,γ)]. (orig./HSI)