Geometrization of metric boundary data for Einstein's equations

Abstract

The principle part of Einstein equations in the harmonic gauge consists of a constrained system of 10 curved space wave equations for the components of the space-time metric. A well-posed initial boundary value problem based upon a new formulation of constraint-preserving boundary conditions of the Sommerfeld type has recently been established for such systems. In this paper these boundary conditions are recast in a geometric form. This serves as a first step toward their application to other metric formulations of Einstein's equations.

Article to appear in Gen. Rel. Grav. volume in memory of Juergen Ehlers

References in corpus (6)

• On the Numerical Integration of Einstein's Field Equations
• Fully General Relativistic Simulations of Black Hole-Neutron Star Mergers
• Problems which are well-posed in a generalized sense with applications to the Einstein equations
• 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
• Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations

Cited by in corpus (8)

• Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
• The Initial-Boundary Value Problem in General Relativity
• Globally hyperbolic spacetimes: slicings, boundaries and counterexamples
• Boundary Conditions for the Gravitational Field
• Constraint-preserving boundary conditions in the 3+1 first-order approach
• Disembodied boundary data for Einstein's equations
• Geometric Boundary Data for the Gravitational Field
• Gowdy waves as a test-bed for constraint-preserving boundary conditions