"Event and Apparent Horizon Finders
for 3 + 1 Numerical Relativity"
by
Jonathan Thornburg
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Abstract
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
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
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
Footnotes
Figures