Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations
arXiv:gr-qc/0611010
Abstract
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.
References in corpus (23)
- On the Numerical Integration of Einstein's Field Equations
- Extending the lifetime of 3D black hole computations with a new hyperbolic system of evolution equations
- Fixing Einstein's equations
- Well-Posed Initial-Boundary Evolution in General Relativity
- First-order symmetric-hyperbolic Einstein equations with arbitrary fixed gauge
- First order hyperbolic formalism for Numerical Relativity
- Critical Collapse of the Massless Scalar Field in Axisymmetry
- Well posed constraint-preserving boundary conditions for the linearized Einstein equations
- Boundary conditions in linearized harmonic gravity
- Constraint-preserving boundary conditions in numerical relativity
- Boundary Conditions for the Einstein Evolution System
- Optimal Constraint Projection for Hyperbolic Evolution Systems
- Numerical Tests of Evolution Systems, Gauge Conditions, and Boundary Conditions for 1D Colliding Gravitational Plane Waves
- Geometrical Hyperbolic Systems for General Relativity and Gauge Theories
- Extended Lifetime in Computational Evolution of Isolated Black Holes
- Controlling the Growth of Constraints in Hyperbolic Evolution Systems
- Einstein boundary conditions for the 3+1 Einstein equations
- Boundary conditions for hyperbolic formulations of the Einstein equations
- Einstein boundary conditions in relation to constraint propagation for the initial-boundary value problem of the Einstein equations
- First-order quasilinear canonical representation of the characteristic formulation of the Einstein equations
- Gauge fixing for the simulation of black hole spacetimes
- Constraint Preserving Boundary Conditions for Hyperbolic Formulations of Einstein's Equations
- Constraint preserving boundary conditions for the linearized BSSN formulation