Boundary conditions for hyperbolic formulations of the Einstein equations

Abstract

In regards to the initial-boundary value problem of the Einstein equations, we argue that the projection of the Einstein equations along the normal to the boundary yields necessary and appropriate boundary conditions for a wide class of equivalent formulations. We explicitly show that this is so for the Einstein-Christoffel formulation of the Einstein equations in the case of spherical symmetry.Comment: 15 pages; text added and typesetting errors corrected; to appear in Classical and Quantum Gravit