, Volume 14, Issue 5, pp 1109-1134

Gluing Construction of Initial Data with Kerr–de Sitter Ends

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Abstract

We construct initial data sets which satisfy the vacuum constraint equations of General Relativity with positive cosmological constant. More precisely, we deform initial data with ends asymptotic to Schwarzschild–de Sitter to obtain non-trivial initial data with exactly Kerr–de Sitter ends. The method is inspired from Corvino’s gluing method. We obtain here a extension of a previous result for the time-symmetric case by Chruściel and Pollack (Ann H Poincaré 9(4):639–654, 2008). We also deal with the case of asymptotically Kerr–de Sitter initial data.

Communicated by Krzysztof Gawedzki.