Living Reviews in Relativity

"Event and Apparent Horizon Finders
for 3 + 1 Numerical Relativity"
Jonathan Thornburg  

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Part I: Introduction
1 Notation and Terminology
2 2-Surface Parameterizations
2.1 Level-set-function parameterizations
2.2 Strahlkörper parameterizations
2.3 Finite-element parameterizations
3 Software-Engineering Issues
3.1 Software libraries and toolkits
3.2 Code reuse and sharing
3.3 Using multiple event/apparent horizon finders
Part II: Finding Event Horizons
4 Introduction
5 Algorithms and Codes for Finding Event Horizons
5.1 Integrating null geodesics forwards in time
5.2 Integrating null geodesics backwards in time
5.3 Integrating null surfaces backwards in time
6 Summary of Algorithms/Codes for Finding Event Horizons
Part III: Finding Apparent Horizons
7 Introduction
7.1 Definition
7.2 General properties
7.3 Trapping, isolated, and dynamical horizons
7.4 Description in terms of the 3 + 1 variables
7.5 Geometry interpolation
7.6 Criteria for assessing algorithms
7.7 Local versus global algorithms
8 Algorithms and Codes for Finding Apparent Horizons
8.1 Zero-finding in spherical symmetry
8.2 The shooting algorithm in axisymmetry
8.3 Minimization algorithms
8.4 Spectral integral-iteration algorithms
8.5 Elliptic-PDE algorithms
8.6 Horizon pretracking
8.7 Flow algorithms
9 Summary of Algorithms/Codes for Finding Apparent Horizons
10 Acknowledgements
A Solving a Single Nonlinear Algebraic Equation
B The Numerical Integration of Ordinary Differential Equations
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