Cactus Code Thorn AHFinder
Author(s)    : Erik Schnetter <[email protected]>
Maintainer(s): Erik Schnetter <[email protected]>
Licence      : LGPL
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1. Purpose

Find apparent horizons



2. Method

See Gundlach.



2.1. Variables and equations

g_ab(\theta, \phi)

\Gamma^a_bc = 1/2 g^ad (g_dc,b + g_bd,c - g_bc,d)

h(\theta, \phi)

F(r, \theta, \phi) = r - h(\theta, \phi)

s_a = \partial_a F / \sqrt{ g^ab (\partial_a F) (\partial_b F) }

s^a;a = \partial_a s^a + \Gamma^a_ab s^b

\Theta = s^a;a - (g^ab - s^a s^b) K_ab



2.2. Discretization basis

Spin-weighted spherical harmnoics:

s_Y_lm(\theta, \phi)



3. References

Jonathan Thornburg, "Finding Apparent Horizons in Numerical
Relativity", arXiv:gr-qc/9508014

Carsten Gundlach, "Pseudo-spectral apparent horizon finders: an
efficient new algorithm", arXiv:gr-qc/9707050

Jonathan Thornburg, "A Fast Apparent-Horizon Finder for 3-Dimensional
Cartesian Grids in Numerical Relativity", arXiv:gr-qc/0306056

Jonathan Thornburg, "Event and Apparent Horizon Finders for 3+1
Numerical Relativity", arXiv:gr-qc/0512169

Lap-Ming Lin, Jerome Novak, "A new spectral apparent horizon finder
for 3D numerical relativity", arXiv:gr-qc/0702038



<https://en.wikipedia.org/wiki/Spin-weighted_spherical_harmonics>
<https://en.wikipedia.org/wiki/Vector_spherical_harmonics>



libsharp: 

- supports arbitrary spins

Martin Reinecke, Dag Sverre Seljebotn, "Libsharp - spherical harmonic
transforms revisited", arXiv:1303.4945 [physics.comp-ph]]

<https://gitlab.mpcdf.mpg.de/mtr/libsharp>, previously
<https://github.com/Libsharp/libsharp>



SHTOOLS:

- only scalars

Mark A. Wieczorek and Matthias Meschede (2018). SHTools -- Tools for
working with spherical harmonics, Geochemistry, Geophysics,
Geosystems, 19, 2574-2592, doi:10.1029/2018GC007529.

<https://shtools.github.io/SHTOOLS/>



ssht:

- use spin weights

J. D. McEwen, Y. Wiaux, "A novel sampling theorem on the sphere",
arXiv:1110.6298 [cs.IT]

<http://astro-informatics.github.io/ssht/>