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
3.5 3D characteristic evolution
3.6 Characteristic treatment of binary black holes
3.7 Perturbations of Schwarzschild
3.8 Nonlinear mode coupling
3.9 3D Einstein-Klein-Gordon system
4 Cauchy-Characteristic Matching
4.1 Computational boundaries
4.2 The computational matching strategy
4.3 Perturbative matching schemes
4.4 Cauchy-characteristic matching for 1D gravitational systems
4.5 Axisymmetric Cauchy-characteristic matching
4.6 Cauchy-characteristic matching for 3D scalar waves
4.7 Stable implementation of 3D linearized Cauchy-characteristic matching
4.8 The binary black hole inner boundary
5 Numerical Hydrodynamics on Null Cones
5.1 Spherically symmetric hydrodynamic codes
5.2 Axisymmetric characteristic hydrodynamic simulations
5.3 Three-dimensional characteristic hydrodynamic simulations
Acknowledgments
Open References References
Figures