Implementation of higher-order absorbing boundary conditions for the Einstein equations
arXiv:0811.3593 · doi:10.1088/0264-9381/26/7/075009
Abstract
We present an implementation of absorbing boundary conditions for the Einstein equations based on the recent work of Buchman and Sarbach. In this paper, we assume that spacetime may be linearized about Minkowski space close to the outer boundary, which is taken to be a coordinate sphere. We reformulate the boundary conditions as conditions on the gauge-invariant Regge-Wheeler-Zerilli scalars. Higher-order radial derivatives are eliminated by rewriting the boundary conditions as a system of ODEs for a set of auxiliary variables intrinsic to the boundary. From these we construct boundary data for a set of well-posed constraint-preserving boundary conditions for the Einstein equations in a first-order generalized harmonic formulation. This construction has direct applications to outer boundary conditions in simulations of isolated systems (e.g., binary black holes) as well as to the problem of Cauchy-perturbative matching. As a test problem for our numerical implementation, we consider linearized multipolar gravitational waves in TT gauge, with angular momentum numbers l=2 (Teukolsky waves), 3 and 4. We demonstrate that the perfectly absorbing boundary condition B_L of order L=l yields no spurious reflections to linear order in perturbation theory. This is in contrast to the lower-order absorbing boundary conditions B_L with L<l, which include the widely used freezing-Psi_0 boundary condition that imposes the vanishing of the Newman-Penrose scalar Psi_0.
25 pages, 9 figures. Minor clarifications. Final version to appear in Class. Quantum Grav.
References in corpus (30)
- Gravitational wave extraction from an inspiraling configuration of merging black holes
- Inspiral, merger and ringdown of unequal mass black hole binaries: a multipolar analysis
- High-accuracy comparison of numerical relativity simulations with post-Newtonian expansions
- Model Waveform Accuracy Standards for Gravitational Wave Data Analysis
- A New Generalized Harmonic Evolution System
- High-accuracy waveforms for binary black hole inspiral, merger, and ringdown
- Solving Einstein's Equations With Dual Coordinate Frames
- Reducing phase error in long numerical binary black hole evolutions with sixth order finite differencing
- Gauge invariant perturbations of Schwarzschild black holes in horizon-penetrating coordinates
- Gravitational wave extraction and outer boundary conditions by perturbative matching
- Stable radiation-controlling boundary conditions for the generalized harmonic Einstein equations
- Testing outer boundary treatments for the Einstein equations
- Foundations of multiple black hole evolutions
- Characteristic Evolution and Matching
- Accurate Evolution of Orbiting Binary Black Holes
- Boundary Conditions for the Einstein Evolution System
- Problems which are well-posed in a generalized sense with applications to the Einstein equations
- Multipolar analysis of spinning binaries
- Cauchy-perturbative matching and outer boundary conditions: computational studies
- Numerical Tests of Evolution Systems, Gauge Conditions, and Boundary Conditions for 1D Colliding Gravitational Plane Waves
- Cauchy-perturbative matching and outer boundary conditions I: Methods and tests
- Improved outer boundary conditions for Einstein's field equations
- Towards absorbing outer boundaries in General Relativity
- 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
- Rapid Evaluation of Radiation Boundary Kernels for Time-domain Wave Propagation on Blackholes
- Absorbing boundary conditions for simulation of gravitational waves with spectral methods in spherical coordinates
- Analytic structure of radiation boundary kernels for blackhole perturbations
- Explicit solution of the linearized Einstein equations in TT gauge for all multipoles
- Cauchy-perturbative matching revisited: tests in spherical symmetry
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