Asymptotic simplicity is shown to be k‐stable (k≥3) at any Minkowski metric on R4 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 R4 whose conformal curvature tensors result from prescribing zero initial data on past null infinity.
This is the published version, also available here: http://dx.doi.org/10.1063/1.1666825.
Lerner, David E. & Porter, J. R. "Asymptotically simple space-time manifolds." J. Math. Phys. 15, 1416 (1974). http://dx.doi.org/10.1063/1.1666825.