"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
References
Updates
Figures