It is demonstrated that initial data sufficiently close to De-Sitter data develop into solutions of Einstein's equations Ric[g]=Λg with positive cosmological constant Λ, which are asymptotically simple in the past as well as in the future, whence null geodesically complete. Furthermore it is shown that hyperboloidal initial data (describing hypersurfaces which intersect future null infinity in a space-like two-sphere), which are sufficiently close to Minkowskian hyperboloidal data, develop into future asymptotically simple whence null geodesically future complete solutions of Einstein's equations Ric[g]=0, for which future null infinity forms a regular cone with vertexi + that represents future time-like infinity.
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Fachbereich Maschinenbau, Universität der Bundeswehr Hamburg, Holstenhofweg 85, D-2000, Hamburg 70, Federal Republic of Germany
Helmut Friedrich
Communicated by C. H. Taubes
About this article Cite this articleFriedrich, H. On the existence ofn-geodesically complete or future complete solutions of Einstein's field equations with smooth asymptotic structure. Commun.Math. Phys. 107, 587–609 (1986). https://doi.org/10.1007/BF01205488
Received: 01 April 1986
Issue Date: December 1986
DOI: https://doi.org/10.1007/BF01205488
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