Characteristic evolution and matching

DOI10.12942/lrr-2009-3zbMath1166.83300arXiv0810.1903OpenAlexW4210961531WikidataQ30364006 ScholiaQ30364006MaRDI QIDQ5902044

Jeffrey Winicour

Publication date: 8 June 2009

Published in: Living Reviews in Relativity (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.1903

Mathematics Subject Classification ID

Einstein's equations (general structure, canonical formalism, Cauchy problems) (83C05) Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory (83-02) Computational methods for problems pertaining to relativity and gravitational theory (83-08)

Related Items

Taub-NUT from the Dirac monopole ⋮ Unstable horizons and singularity development in holography ⋮ A symmetric hyperbolic formulation of the vacuum Einstein equations in affine-null coordinates

Uses Software

• AHFinderDirect

Cites Work

• Continuous self-similarity and S -duality
• On the global initial value problem and the issue of singularities
• Characteristic evolutions in numerical relativity using six angular patches
• Linearized solutions of the Einstein equations within a Bondi–Sachs framework, and implications for boundary conditions in numerical simulations
• 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
• Problems which are well posed in a generalized sense with applications to the Einstein equations
• A Method for Generating Solutions of Einstein's Equations
• Gauge-invariant non-spherical metric perturbations of Schwarzschild black-hole spacetimes
• Gravitational wave extraction based on Cauchy–characteristic extraction and characteristic evolution
• Asymptotic Symmetries in Gravitational Theory
• General Relativity
• Numerical Methods in Fluid Dynamics
• Numerical approaches to spacetime singularities
• Local and global existence theorems for the Einstein equations
• Numerical hydrodynamics in general relativity
• Critical phenomena in gravitational collapse
• Conformal infinity
• Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Comparison between Darcy and Brinkman laws in a fracture
• On characteristic initial-value and mixed problems
• ``Free-space boundary conditions for the time dependent wave equation
• Cauchy problems for the conformal vacuum field equations in general relativity
• Non-reflecting boundary conditions
• Absorbing boundary conditions for second-order hyperbolic equations
• Nonparametric confidence intervals for population variance of one sample and the difference of variances of two samples
• Time dependent boundary conditions for hyperbolic systems
• A study of nonlinear radiation damping by matching analytic and numerical solutions
• A comparative study of absorbing boundary conditions
• Numerical codes for cylindrical general relativistic systems
• Boundary conditions for time dependent problems with an artificial boundary
• Approximation of radiation boundary conditions
• Evolution of scalar fields from characteristic data
• Absorbing boundary conditions, difference operators, and stability
• Nonreflecting boundary conditions for nonlinear hyperbolic systems
• A dissipative algorithm for wave-like equations in the characteristic formulation
• The instability of naked singularities in the gravitational collapse of a scalar field.
• The initial boundary value problem for Einstein's vacuum field equation
• Cauchy-characteristic evolution and waveforms
• Nonreflecting boundary conditions for Maxwell's equations
• Well posed constraint-preserving boundary conditions for the linearized Einstein equations
• A mathematical theory of gravitational collapse
• Examples of naked singularity formation in the gravitational collapse of a scalar field
• Adaptive mesh refinement for characteristic codes
• The ``cubed sphere: A new method for the solution of partial differential equations in spherical geometry
• Gravitational collapse of a charged and radiating fluid ball in the diffusion limit
• Preparation and tomographic reconstruction of an arbitrary single-photon path qubit
• Boundary conditions for coupled quasilinear wave equations with application to isolated systems
• On the stability of non-autonomous perturbed Lotka-Volterra models
• MATCHING CHARACTERISTIC CODES: EXPLOITING TWO DIRECTIONS
• Wave tails in non-trivial backgrounds
• Well-posed initial-boundary evolution in general relativity
• Collapse of charged scalar fields
• Einstein boundary conditions for the 3+1 Einstein equations
• FEM-analysis of transverse vibrations of an axially moving membrane immersed in ideal fluid
• Gravitational Field of a Particle Falling in a Schwarzschild Geometry Analyzed in Tensor Harmonics
• Gravitational wave forms at finite distances and at null infinity
• Evolution of three-dimensional gravitational waves: Harmonic slicing case
• Numerical integration of Einstein’s field equations
• Reality of the Cylindrical Gravitational Waves of Einstein and Rosen
• Stability of a Schwarzschild Singularity
• Mixed Problems for Linear Systems of first Order Equations
• Gravitational Waves in General Relativity
• The numerical solution of hyperbolic systems of partial differential equations in three independent variables
• Gravitational waves in general relativity VIII. Waves in asymptotically flat space-time
• Gravitational waves in general relativity, VII. Waves from axi-symmetric isolated system
• Numerical relativity. I. The characteristic initial value problem
• Numerical relativity. II. Numerical methods for the characteristic initial value problem and the evolution of the vacuum field equations for space‒times with two Killing vectors
• The formation of black holes and singularities in spherically symmetric gravitational collapse
• Accurate Boundary Conditions for Exterior Problems in Gas Dynamics
• Implementation of standard testbeds for numerical relativity
• Testing outer boundary treatments for the Einstein equations
• Characteristic initial data and wavefront singularities in general relativity
• Newtonian gravity on the null cone
• Absorbing Boundary Conditions for Difference Approximations to the Multi-Dimensional Wave Equation
• An Approach to Gravitational Radiation by a Method of Spin Coefficients
• On the Characteristic Initial Value Problem in Gravitational Theory
• Radiation boundary conditions for wave-like equations
• On the regular and the asymptotic characteristic initial value problem for Einstein’s vacuum field equations
• The asymptotic characteristic initial value problem for Einstein’s vacuum field equations as an initial value problem for a first-order quasilinear symmetric hyperbolic system
• Numerical relativity: combining the Cauchy and characteristic initial value problems
• Dual-null dynamics of the Einstein field
• Absorbing Boundary Conditions for the Numerical Simulation of Waves
• Topological censorship
• Bounded variation solutions of the spherically symmetric einstein‐scalar field equations
• Null cone evolution of axisymmetric vacuum space–times
• The eth formalism in numerical relativity
• Einstein equations in the null quasispherical gauge
• Shear-free null quasi-spherical space–times
• The Kerr spacetime in generalized Bondi–Sachs coordinates
• Towards standard testbeds for numerical relativity
• A fast apparent horizon finder for three-dimensional Cartesian grids in numerical relativity
• Colliding black holes: The close limit
• Black Hole Singularities: A Numerical Approach
• Cauchy-Characteristic Matching: A New Approach to Radiation Boundary Conditions
• Structure of the Black Hole's Cauchy-Horizon Singularity
• Numerical Methods for the Einstein Equations in Null Quasi-Spherical Coordinates
• Cauchy-characteristic matching for a family of cylindrical solutions possessing both gravitational degrees of freedom
• Quasi-spherical light cones of the Kerr geometry
• The Cauchy problem and the initial boundary value problem in numerical relativity
• Self-similar and charged spheres in the diffusion approximation
• Well-Posedness of One-Way Wave Equations and Absorbing Boundary Conditions
• Numerical relativity - III. The Bondi mass revisited
• Black-hole excision with multiple grid patches
• The spherically symmetric collapse of a massless scalar field
• Hyperbolic reductions for Einstein's equations