Boundary Conditions for the Gravitational Field
arXiv:1203.2154 · doi:10.1088/0264-9381/29/11/113001
Abstract
A review of the treatment of boundaries in general relativity is presented with the emphasis on application to the formulations of Einstein's equations used in numerical relativity. At present, it is known how to treat boundaries in the harmonic formulation of Einstein's equations and a tetrad formulation of the Einstein-Bianchi system. However, a universal approach valid for other formulations is not in hand. In particular, there is no satisfactory boundary theory for the 3+1 formulations which have been highly successful in binary black hole simulation. I discuss the underlying problems that make the initial-boundary value problem much more complicated than the Cauchy problem. I review the progress that has been made and the important open questions that remain.
Some clarification added and typos corrected. Final version to appear in Classical and Quantum Gravity
References in corpus (26)
- Total recoil: the maximum kick from nonspinning black-hole binary inspiral
- Fully General Relativistic Simulations of Black Hole-Neutron Star Mergers
- Simulation of Binary Black Hole Spacetimes with a Harmonic Evolution Scheme
- Relativistic Simulations of Black Hole-Neutron Star Mergers: Effects of black-hole spin
- Well-posedness of formulations of the Einstein equations with dynamical lapse and shift conditions
- Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations
- Testing outer boundary treatments for the Einstein equations
- An explicit harmonic code for black-hole evolution using excision
- Hyperboloidal evolution with the Einstein equations
- Hyperboloidal Einstein-matter evolution and tails for scalar and Yang-Mills fields
- Implementation of standard testbeds for numerical relativity
- Regularity of the Einstein Equations at Future Null Infinity
- Improved outer boundary conditions for Einstein's field equations
- Towards absorbing outer boundaries in General Relativity
- Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
- Boundary conditions for coupled quasilinear wave equations with application to isolated systems
- Initial boundary value problems for Einstein's field equations and geometric uniqueness
- 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
- Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations
- Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations
- The Initial-Boundary Value Problem in General Relativity
- 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
- Geometrization of metric boundary data for Einstein's equations
- The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves
Cited by in corpus (6)
- Three-Dimensional General-Relativistic Hydrodynamic Simulations of Binary Neutron Star Coalescence and Stellar Collapse with Multipatch Grids
- Globally hyperbolic spacetimes: slicings, boundaries and counterexamples
- Including realistic tidal deformations in binary black-hole initial data
- Constraint preserving boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura formulation in spherical symmetry
- Geometric Boundary Data for the Gravitational Field
- Dynamics of Nonlinear Waves on Bounded Domains