The initial value problem for radiating space-times

Abstract

The question of linearisation stability of the constraint equations for asymptotically simple space-times is examined, with the data given on a hypersurface of constant mean extrinsic curvature. It is shown that there exist solutions of the constraint equations. These solutions correspond to initial data lying in a functional neighbourhood of the solution corresponding to the data given by the intrinsic and extrinsic curvature tensors of a hyperboloid in Minkowski space. The linearized equations are examined and it is shown explicitly how these may be solved in terms of Green's functions.