Boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations
arXiv:0910.5763 · doi:10.1103/PhysRevD.81.044011
Abstract
We discuss the initial-boundary value problem for the Baumgarte-Shapiro-Shibata-Nakamura evolution system of Einstein's field equations which has been used extensively in numerical simulations of binary black holes and neutron stars. We specify nine boundary conditions for this system with the following properties: (i) they impose the momentum constraint at the boundary, which is shown to preserve all the constraints throughout evolution, (ii) they approximately control the incoming gravitational degrees of freedom by specifying the Weyl scalar Psi_0 at the boundary, (iii) they control the gauge freedom by requiring a Neumann boundary condition for the lapse, by setting the normal component of the shift to zero, and by imposing a Sommerfeld-like condition on the tangential components of the shift, (iv) they are shown to yield a well-posed problem in the limit of weak gravity. Possible numerical applications of our results are also discussed briefly.
20 pages, no figures, small corrections in order to match published version
References in corpus (19)
- How to move a black hole without excision: gauge conditions for the numerical evolution of a moving puncture
- Reducing orbital eccentricity in binary black hole simulations
- Testing outer boundary treatments for the Einstein equations
- Excision without excision: the relativistic turducken
- Hyperboloidal evolution with the Einstein equations
- An axisymmetric evolution code for the Einstein equations on hyperboloidal slices
- Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills fields
- Regularity of the Einstein Equations at Future Null Infinity
- Spacelike matching to null infinity
- Implementation of higher-order absorbing boundary conditions for the Einstein equations
- Gravitational perturbations of Schwarzschild spacetime at null infinity and the hyperboloidal initial value problem
- Improved outer boundary conditions for Einstein's field equations
- Towards absorbing outer boundaries in General Relativity
- Black hole initial data on hyperboloidal slices
- Boundary conditions for coupled quasilinear wave equations with application to isolated systems
- Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates
- Outer boundary conditions for Einstein's field equations in harmonic coordinates
- Absorbing boundary conditions for Einstein's field equations
- A minimization problem for the lapse and the initial-boundary value problem for Einstein's field equations
Cited by in corpus (15)
- Binary Neutron Star Mergers
- Compact binary evolutions with the Z4c formulation
- Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
- Constraint preserving boundary conditions for the Z4c formulation of general relativity
- Numerical stability of the Z4c formulation of general relativity
- Numerical simulations with a first order BSSN formulation of Einstein's field equations
- Discontinuous Galerkin method for the spherically reduced BSSN system with second-order operators
- Exploring the Outer Limits of Numerical Relativity
- Hyperboloidal evolution of test fields in three spatial dimensions
- The Initial-Boundary Value Problem in General Relativity
- Boundary Conditions for the Gravitational Field
- Constraint-preserving boundary conditions in the 3+1 first-order approach
- Disembodied boundary data for Einstein's equations
- The initial boundary value problem for free-evolution formulations of General Relativity
- Constraint preserving boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura formulation in spherical symmetry