This project implements an algorithm for numerically finding MOTSs that are not star-shaped. The current implementation is limited to the axisymmetric case but the ideas it is based on easily generalize to the fully non-symmetrical case.

Anyone is free and welcome to use the code provided in this project (see the LICENSE.txt). For any publications produced using this code, please cite:

D. Pook-Kolb, O. Birnholtz, B. Krishnan and E. Schnetter "Existence and stability of marginally trapped surfaces in black-hole spacetimes." Physical Review D 99.6 (2019): 064005.

For any questions/comments/ideas, feel free to contact daniel.pook.kolb at aei.mpg.de.

HTML documentation (including this readme) is available online or can be generated from the current source (see README_SRC.md).

NOTE

If a class method is not documented, check if the parent class one is instead.

Some of the below links only work in the online version of this help.

• Brill-Lindquist initial data
• Using the finder with a numerical metric
• Using the shooting method (html, notebook)
• Finding stability spectra in Kerr slices (html, notebook)
• Implementing a new analytical metric (html, notebook)

The prerequisites for running the MOTS Finder are as follows (indicated package versions have been tested, newer versions work in most cases):

• Python 3.6, 3.7, 3.8, 3.9
• SciPy 1.2.1
• NumPy 1.16.1
• SymPy 1.3
• mpmath 1.1.0
• matplotlib 2.2.5
• Jupyter
• Optionally, for speeding up several computations, cython 0.29.15
• Optionally, for reading simulation data: SimulationIO with its prerequisites and Python 3 bindings
• Optionally, for expansions into spin-weighted spherical harmonics: spinsfast with its prerequisites

The simplest way to set up the environment on a Linux-based machine is as follows. Here, we use apt (e.g. in Ubuntu), please translate to your preferred package management method.

First, create a new Python environment to not interfere with any of your system Python configurations:

$ sudo apt install virtualenv
$ cd ~
$ virtualenv --always-copy --python=python3 py3env

Next, clone this repo to get the MOTS Finder source code:

$ mkdir -p ~/src
$ cd ~/src
$ git clone https://github.com/daniel-dpk/distorted-motsfinder-public.git

Finally, install all the required Python packages:

$ source ~/py3env/bin/activate
$ pip install -r ~/src/distorted-motsfinder-public/python-requirements.txt

To use the finder, start a notebook server in a dedicated folder:

$ source ~/py3env/bin/activate  # in case it's not already active
$ mkdir -p ~/src/motsfinder-local-notebooks
$ cd ~/src/motsfinder-local-notebooks
$ jupyter notebook

NOTE: If you already use Jupyter from a different Python environment, the above will probably override your system Jupyter settings. To avoid that, replace the last line with:

$ JUPYTER_CONFIG_DIR="$HOME/.jupyter-motsfinder" JUPYTER_DATA_DIR="$HOME/.local/share/jupyter-motsfinder" jupyter notebook

Likewise, to install the Jupyter extensions into this environment, execute the following and then restart the Jupyter notebook server using the above command:

$ source ~/py3env/bin/activate  # in case it's not already active
$ JUPYTER_CONFIG_DIR="$HOME/.jupyter-motsfinder" JUPYTER_DATA_DIR="$HOME/.local/share/jupyter-motsfinder" jupyter contrib nbextension install --user

A short summary of the required steps to utilize the Cython implementations is:

$ sudo apt install python3-dev
$ source ~/py3env/bin/activate
$ cd ~/src/distorted-motsfinder-public
$ pip install cython
$ ./cythonize_helper.py

If you need to read simulation data and would like to use SimulationIO for this purpose, please see its instructions for building and installation.

The following works on Ubuntu-based systems. Please translate to your environment as needed.

$ sudo apt install libfftw3-dev
... restart shell ...
$ source ~/py3env/bin/activate
$ pip install spinsfast

Maintainer: Daniel Pook-Kolb

Further authors and contributors:

• Ofek Birnholtz
• Ivan Booth
• Robie A. Hennigar
• Jose Luis Jaramillo
• Badri Krishnan
• Erik Schnetter
• Victor Zhang

An overview of how the project source is organized and documented is available in README_SRC.md.