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
References
http://www.livingreviews.org/lrr-2007-3
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