Abstract:
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 ℝn (n≥ 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.
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Received: 8 November 1999 / Accepted: 27 March 2000
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Corvino, J. Scalar Curvature Deformation and a Gluing Construction for the Einstein Constraint Equations. Commun. Math. Phys. 214, 137–189 (2000). https://doi.org/10.1007/PL00005533
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DOI: https://doi.org/10.1007/PL00005533