Scalar Curvature Deformation and a Gluing Construction for the Einstein Constraint Equations
Scalar Curvature Deformation and a Gluing
Construction for the Einstein Constraint Equations
摘要：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 flflat, scalar-flflat metrics on Rn (n ≥ 3) which are spherically symmetric, hence Schwarzschild, at infifinity, 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 infifinity.