We study the stability of the Penrose compactification for solutions of the vacuum Einstein equation, in the context of the time-symmetric initial-value problem. The initial data (R-3, g) must satisfy the Hamiltonian constraint R(g) = 0, and we consider perturbations about the Euclidean metric arising from tensors h satisfying the equation L(h) = 0, where L is the linearization of the scalar curvature operator at the Euclidean metric. We show that each member h of a large family of compactly supported solutions of the linearized problem is tangent to a curve (g) over bar (epsilon) of solutions to the nonlinear constraint, so that each metric (g) over bar (epsilon), along the curve evolves under the vacuum Einstein equation to a spacetime which is asymptotically simple in the sense of Penrose.
Title
On the existence and stability of the Penrose compactification