J. Corvino

Title: Gluing solutions: non-conformal approach

Abstract: We discuss constructing asymptotically flat (AF) solutions of the constraint equations by a gluing procedure. In contrast to the conformal method, we use the full underdetermined-elliptic nature of the constraint operator. Given an AF solution of the constraints (vacuum time-symmetric, full vacuum constraints, or Einstein-Maxwell) we glue in a suitably chosen member of a model family near infinity (e.g. Schwarzschild, Kerr, Reissner-Nordstrom) and compactly perturb to a solution of the constraints. The model family at infinity is chosen to have enough free parameters to account for the kernel of the adjoint of the linearized constraint operator at the flat data; this kernel determines what part of the asymptotics is essentially determined by the constraints, and corresponds naturally to the energy-momentum, angular momentum-center-of-mass, and total charge. The case of the full vacuum constraints is joint work with R.M.Schoen (gr-qc/0301071)

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Copyright 29.VIII.02 by P.T.Chrusciel, A.Chopin, and J. Corvino