Living Reviews in Relativity

"Characteristic Evolution and Matching"
by
Jeffrey Winicour  

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Abstract
1 Introduction
2 The Characteristic Initial Value Problem
3 Prototype Characteristic Evolution Codes
3.1 {1 + 1}-dimensional codes
3.2 {2 + 1}-dimensional codes
3.3 The Bondi problem
3.4 The Bondi mass
4 3D Characteristic Evolution
4.1 Coordinatization of the sphere
4.2 Geometrical formalism
4.3 Characteristic treatment of binary black holes
4.4 Perturbations of Schwarzschild
4.5 Nonlinear mode coupling
4.6 3D Einstein–Klein–Gordon system
5 Cauchy-Characteristic Matching
5.1 Computational boundaries
5.2 The computational matching strategy
5.3 The outer Cauchy boundary in numerical relativity
5.4 Perturbative matching schemes
5.5 Cauchy-characteristic matching for 1D gravitational systems
5.6 Axisymmetric Cauchy-characteristic matching
5.7 Cauchy-characteristic matching for 3D scalar waves
5.8 Stable 3D linearized Cauchy-characteristic matching
5.9 The binary black hole inner boundary
6 Cauchy-Characteristic Extraction of Waveforms
7 Numerical Hydrodynamics on Null Cones
7.1 Spherically symmetric hydrodynamic codes
7.2 Axisymmetric characteristic hydrodynamic simulations
7.3 Three-dimensional characteristic hydrodynamic simulations
Acknowledgments
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