Characteristic Evolution and Matching
arXiv:0810.1903 · doi:10.12942/lrr-2009-3
Abstract
I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress in characteristic evolution is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to extend such simulations to null infinity where the waveform from the binary inspiral and merger can be unambiguously computed. This has now been accomplished by Cauchy-characteristic extraction, where data for the characteristic evolution is supplied by Cauchy data on an extraction worldtube inside the artificial outer boundary. The ultimate application of characteristic evolution is to eliminate the role of this outer boundary by constructing a global solution via Cauchy-characteristic matching. Progress in this direction is discussed.
New version to appear in Living Reviews 2012. arXiv admin note: updated version of arXiv:gr-qc/0508097
References in corpus (46)
- Model Waveform Accuracy Standards for Gravitational Wave Data Analysis
- Critical phenomena in gravitational collapse
- Binary black hole merger dynamics and waveforms
- Simulations of Binary Black Hole Mergers Using Spectral Methods
- Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
- Dynamics and Gravitational Wave Signature of Collapsar Formation
- Unambiguous determination of gravitational waveforms from binary black hole mergers
- Testing outer boundary treatments for the Einstein equations
- Characteristic extraction in numerical relativity: binary black hole merger waveforms at null infinity
- Gravitational memory in binary black hole mergers
- Gravitational Wave Extraction in Simulations of Rotating Stellar Core Collapse
- Gravitational-wave detectability of equal-mass black-hole binaries with aligned spins
- Stability of general-relativistic accretion disks
- A Characteristic Extraction Tool for Gravitational Waveforms
- A complete gauge-invariant formalism for arbitrary second-order perturbations of a Schwarzschild black hole
- A numerical study of the quasinormal mode excitation of Kerr black holes
- Problems which are well-posed in a generalized sense with applications to the Einstein equations
- Black Hole Excision with Multiple Grid Patches
- Implementation of standard testbeds for numerical relativity
- Dealing with delicate issues in waveforms calculations
- Strategies for the Characteristic Extraction of Gravitational Waveforms
- How far away is far enough for extracting numerical waveforms, and how much do they depend on the extraction method?
- Numerical relativity with characteristic evolution, using six angular patches
- Mode coupling of Schwarzschild perturbations: Ringdown frequencies
- Boundary conditions for coupled quasilinear wave equations with application to isolated systems
- Optimal Calibration Accuracy for Gravitational Wave Detectors
- Well-posed initial-boundary value problem for the harmonic Einstein equations using energy estimates
- Constraint-preserving boundary treatment for a harmonic formulation of the Einstein equations
- Constraint-preserving Sommerfeld conditions for the harmonic Einstein equations
- Outer boundary conditions for Einstein's field equations in harmonic coordinates
- Improved Time-Domain Accuracy Standards for Model Gravitational Waveforms
- A framework for large-scale relativistic simulations in the characteristic approach
- Use and Abuse of the Model Waveform Accuracy Standards
- On characteristic initial data for a star orbiting a black hole
- Binary Black Hole Waveform Extraction at Null Infinity
- Initial data transients in binary black hole evolutions
- The Initial-Boundary Value Problem in General Relativity
- Absorbing boundary conditions for Einstein's field equations
- Gravitational Instability of a Kink
- Central equation of state in spherical characteristic evolutions
- Solving the Einstein constraint equations on multi-block triangulations using finite element methods
- Observational cosmology using characteristic numerical relativity
- Worldtube conservation laws for the null-timelike evolution problem
- Estimating total momentum at finite distances
- The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves
- Bondian frames to couple matter with radiation
Cited by in corpus (43)
- Surrogate model of hybridized numerical relativity binary black hole waveforms
- Fast and accurate prediction of numerical relativity waveforms from binary black hole coalescences using surrogate models
- Agnostic black hole spectroscopy: Quasinormal mode content of numerical relativity waveforms and limits of validity of linear perturbation theory
- Continuum and Discrete Initial-Boundary-Value Problems and Einstein's Field Equations
- Null infinity waveforms from extreme-mass-ratio inspirals in Kerr spacetime
- Three-Dimensional General-Relativistic Hydrodynamic Simulations of Binary Neutron Star Coalescence and Stellar Collapse with Multipatch Grids
- A Characteristic Extraction Tool for Gravitational Waveforms
- Defining eccentricity for gravitational wave astronomy
- Brans-Dicke theory in Bondi-Sachs form: Asymptotically flat solutions, asymptotic symmetries and gravitational-wave memory effects
- Spherical symmetry as a test case for unconstrained hyperboloidal evolution
- Tetrad formalism for numerical relativity on conformally compactified constant mean curvature hypersurfaces
- Black hole initial data on hyperboloidal slices
- Gravitational-wave echoes from numerical-relativity waveforms via space-time construction near merging compact objects
- Gravitational waves in dynamical spacetimes with matter content in the Fully Constrained Formulation
- A geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad
- Taub-NUT from the Dirac monopole
- Boundary conditions for the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's field equations
- Unconstrained hyperboloidal evolution of black holes in spherical symmetry with GBSSN and Z4c
- Spherically symmetric black hole spacetimes on hyperboloidal slices
- Adaptive Mesh Refinement for Characteristic Grids
- Central equation of state in spherical characteristic evolutions
- Numerical Evolution of axisymmetric vacuum spacetimes: a code based on the Galerkin method
- Nonadiabatic charged spherical evolution in the postquasistatic approximation
- Observational cosmology using characteristic numerical relativity
- Observational cosmology using characteristic numerical relativity: Characteristic formalism on null geodesics
- Optimizing post-Newtonian parameters and fixing the BMS frame for numerical-relativity waveform hybridizations
- The Well-posedness of the Null-Timelike Boundary Problem for Quasilinear Waves
- Scalar field as a time variable during gravitational evolution
- Bondian frames to couple matter with radiation
- Bondi-Sachs Energy-Momentum for the CMC Initial Value Problem
- Einstein-Klein-Gordon system via Cauchy-characteristic evolution: Computation of memory and ringdown tail
- Where is the ringdown? Reconstructing quasinormal modes from dispersive waves
- Simulations of gravitational collapse in null coordinates: I. Formulation and weak-field tests in generalised Bondi gauges
- Shear Viscosity in the Post-quasistatic Approximation
- Gravitational-wave memory effects in the Damour-Esposito-Farèse extension of Brans-Dicke theory
- Testing the well-posedness of characteristic evolution of scalar waves
- Estimating Energy-Momentum and Angular Momentum Near Null Infinity
- Quasinormal modes of a Schwarzschild black hole within the Bondi-Sachs framework
- A Note on the Strong Hyperbolicity of Gravity with Dynamical Shifts
- A symmetric hyperbolic formulation of the vacuum Einstein equations in affine-null coordinates
- Internal structure of Hayward black holes
- Hybrid waveforms for precessing quasi-circular binary systems
- On the falloff of radiated energy in black hole spacetimes