Boundary Conditions en General Relativity

OSCAR REULA; OLIVIER SARBACH; HEINZ-OTTO KREISS; J. WINICOUR

Distrito Federal

Conferencia; 19th International Conference on General Relativity and Gravitation; 2010

International Society on General Relativity and Gravitation

We consider the initial-boundary value problem for systems of quasilinear wave equations on domains of the form $[0,T] imes Sigma$, where $Sigma$ is a compact manifold with smooth boundaries $partialSigma$. By using an appropriate reduction to a first order symmetric hyperbolic system with maximal dissipative boundary conditions, well posedness of such problems is established for a large class of boundary conditions on $partialSigma$. We show that our class of boundary conditions is sufficiently general to allow for a well posed formulation for different wave problems in the presence of constraints and artificial, nonreflecting boundaries, including Maxwell´s equations in the Lorentz gauge and Einstein´s gravitational equations in harmonic coordinates. Our results should also be useful for obtaining stable finite-difference discretizations for such problems.