Asymptotically simple space-time manifolds

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Abstract
Asymptotic simplicity is shown to be k‐stable (k≥3) at any Minkowski metric on R 4 in both the Whitney fine Ck topology and a coarser topology (in which the Ck twice‐convariant symmetric tensors form a Banach manifold whose connected components consist of tensor field asymptotic to one another at null infinity). This result, together with a sequential method for solving the field equations previously proposed by the authors, allows a fairly straightforward proof that a well‐known result in the linearized theory holds in the full nonlinear theory as well: There are no nontrivial (i.e., non‐Minkowskian) asymptotically simple vacuum metrics on R 4 whose conformal curvature tensors result from prescribing zero initial data on past null infinity.

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