
Abstract 
Part I: Introduction 
1 
Notation and Terminology 
2 
2Surface
Parameterizations 

2.1 
Levelsetfunction parameterizations 

2.2 
Strahlkörper
parameterizations 

2.3 
Finiteelement parameterizations 
3 
SoftwareEngineering
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 
Zerofinding in spherical symmetry 

8.2 
The
shooting algorithm in axisymmetry 

8.3 
Minimization algorithms 

8.4 
Spectral
integraliteration algorithms 

8.5 
EllipticPDE 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 