Abstract:We construct compact initial data of constant mean curvature K for Einstein's 4d vacuum equations with Λ = Λ − ( K 2 /3) positive, where Λ is the cosmological constant, via the conformal method. To construct a transverse, trace-free (TT) momentum tensor explicitly we first observe that, if the seed manifold has two orthogonal Killing vectors, their symmetrized tensor product is a natural TT candidate. Without the orthogonality requirement, but on locally conformally flat seed manifolds there is a generalized c… Show more
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