2007/07/31 by Milton Ruiz, Oliver Rinne, Olivier Sarbach
Mathematics · Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Geometric Analysis and Curvature Flows #gr-qc
paper · pdf · doi:10.1088/0264-9381/24/24/012
published as Class.Quant.Grav.24:6349-6378,2007 · Added more details on specifying initial data and the numerical calculation of reflection coefficients. 24 pages, 11 figures. To appear in Classical and Quantum Gravity
arxiv created 2007/11/16 · openalex publication_date 2007/11/29 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
We analyze Einstein's vacuum field equations in generalized harmonic coordinates on a compact spatial domain with boundaries. We specify a class of boundary conditions, which is constraint-preserving and sufficiently general to include recent proposals for reducing the amount of spurious reflections of gravitational radiation. In particular, our class comprises the boundary conditions recently proposed by Kreiss and Winicour, a geometric modification thereof, the freezing-Ψ 0 boundary condition and the hierarchy of absorbing boundary conditions introduced by Buchman and Sarbach. Using the recent technique developed by Kreiss and Winicour based on an appropriate reduction to a pseudo-differential first-order system, we prove well posedness of the resulting initial-boundary value problem in the frozen coefficient approximation. In view of the theory of pseudo-differential operators, it is expected that the full nonlinear problem is also well posed. Furthermore, we implement some of our boundary conditions numerically and study their effectiveness in a test problem consisting of a perturbed Schwarzschild black hole.