11 research outputs found
Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
Specifying boundary conditions continues to be a challenge in numerical
relativity in order to obtain a long time convergent numerical simulation of
Einstein's equations in domains with artificial boundaries. In this paper, we
address this problem for the Einstein--Christoffel (EC) symmetric hyperbolic
formulation of Einstein's equations linearized around flat spacetime. First, we
prescribe simple boundary conditions that make the problem well posed and
preserve the constraints. Next, we indicate boundary conditions for a system
that extends the linearized EC system by including the momentum constraints and
whose solution solves Einstein's equations in a bounded domain
Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations
This paper is concerned with the initial-boundary value problem for the
Einstein equations in a first-order generalized harmonic formulation. We impose
boundary conditions that preserve the constraints and control the incoming
gravitational radiation by prescribing data for the incoming fields of the Weyl
tensor. High-frequency perturbations about any given spacetime (including a
shift vector with subluminal normal component) are analyzed using the
Fourier-Laplace technique. We show that the system is boundary-stable. In
addition, we develop a criterion that can be used to detect weak instabilities
with polynomial time dependence, and we show that our system does not suffer
from such instabilities. A numerical robust stability test supports our claim
that the initial-boundary value problem is most likely to be well-posed even if
nonzero initial and source data are included.Comment: 27 pages, 4 figures; more numerical results and references added,
several minor amendments; version accepted for publication in Class. Quantum
Gra