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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Similar content being viewed by others Explore related subjectsDiscover the latest articles and news from researchers in related subjects, suggested using machine learning. Author information Authors and AffiliationsDepartment of Mathematics, Stanford University, Stanford, CA 94305-2125, USA.¶E-mail: corvino@math.stanford.edu, , , , , , US
Justin Corvino
Received: 8 November 1999 / Accepted: 27 March 2000
About this article Cite this articleCorvino, 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
Issue Date: October 2000
DOI: https://doi.org/10.1007/PL00005533
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