Well-posed initial-boundary evolution in general relativity

Abstract

Maximally dissipative boundary conditions are applied to the initial-boundary value problem for Einstein's equations in harmonic coordinates to show that it is well posed for homogeneous boundary data and for boundary data that is small in a linearized sense. The method is implemented as a nonlinear evolution code, which satisfies convergence tests in the nonlinear regime and is stable in the weak field regime. A linearized version has been stably matched to a characteristic code to compute the gravitational wave form radiated to infinity.