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 underdeterminedelliptic nature of the
constraint operator. Given an AF solution of the constraints
(vacuum timesymmetric, full vacuum constraints, or EinsteinMaxwell) we
glue in a suitably chosen member of a model family near infinity
(e.g. Schwarzschild, Kerr, ReissnerNordstrom) 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
energymomentum, angular momentumcenterofmass, and total charge. The
case of the full vacuum constraints is joint work with R.M.Schoen
(grqc/0301071)

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Corvino's lecture



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