Scalar curvature deformation and a gluing construction for the Einstein constraint equations

On a compact manifold, the scalar curvature map at generic metrics is a local surjection [F-M]. We show that this result may be localized to compact subdomains in an arbitrary Riemannian manifold. The method is extended to establish the existence of asymptotically flat, scalar-flat metrics on R-n (n greater than or equal to 3) which are spherically symmetric, hence Schwarzschild, at infinity, i.e. outside a compact set, Such metrics provide Cauchy data for the Einstein vacuum equations which evolve into nontrivial vacuum spacetimes which are identically Schwarzschild near spatial infinity.