The code used to implement the various animations and diagrams that appear in 2406.11671.
Once you have cloned this repository, you will need to install the dependencies using the Node package manager (https://nodejs.org/en/download/package-manager).
# installs nvm (Node Version Manager)
curl -o- https://raw.githubusercontent.com/nvm-sh/nvm/v0.40.0/install.sh | bash
# download and install Node.js (you may need to restart the terminal)
nvm install 20
# verifies the right Node.js version is in the environment
node -v # should print `v20.17.0`
# verifies the right npm version is in the environment
npm -v # should print `10.8.2`
Once npm is installed, you can install the project dependencies with
npm install
If you have make, you can run an animation using one of the following
make movieOne
make movieTwo
make movieThree
Look inside the Makefile for the commands used to run the animations. There are several command line options that augment the behavior of the animation.
| Option | Values | Description |
|---|---|---|
| VITE_CAPTURESECONDS | Positive integer | Sets the amount of seconds of video capture |
| VITE_CAPTUREON | 0 or 1 | Sets the video capture functionality off or on |
| VITE_MOVIENUMBER | 1,2,3 | Selects one of the three animations |
| VITE_MAXPOINTS | Positive integer | Sets the length of the ray trails |
The movie numbers are described in Animation Descriptions.
To select the embedding diagram animation, uncomment and comment the following lines in index.html.
<!-- <script type="module" src="/main.js"></script> -->
<script type="module" src="/embeddingDiagram.js"></script>
This changes the main javascript file to embeddingDiagram.js rather than
main.js. The value of VITE_MOVIENUMBER is irrelevant when this file is
used.
The javascript files main.js and
embeddingDiagram.js are responsible for rendering
predefined trajectories, which are stored in trajectories/. The
trajectories rendered by main.js are computed in RayTracing.nb while
the trajectories rendered by embeddingDiagram.js are first computed in
EquatorialRays.nb and then transformed into the embedding space in
KerrEmbeddingDiagram.nb. The latter notebook also computes the
embedding diagram itself and exports the geometry to models/.
Below are brief descriptions of the various animations.
Kerr Ray Tracing Subsupercritical: Showcases 3 rays, emitted from the same location but with initial momenta tuned such that one ray falls into the black hole, one ray is bound, and the other is ejected to infinity.
Kerr Ray Tracing Lyapunov: Showcases 3 pairs of rays. In each pair, one of the rays is emitted with momentum such that it is bound, while the other is shot with the same momentum but perturbed slightly in radius by an amount delta r. The separation between the rays in each pair increases as the trajectories undergo an increasing number of half-orbits, with the separation rate determined by the Lyapunov exponent. I have also included a plot of the value of the Lyapunov exponent as one moves radially through the photon sphere, along with the selected radii and corresponding Lyapunov values color coded to match the movie.
Kerr Ray Tracing Equatorial Rays: Shows equatorially orbiting rays about a high-spin black hole that eventually eject to infinity. The rays start in the same position, but one of the rays has a larger initial momentum, leading to more rapid escape.
Kerr Ray Tracing Embedded Equatorial Rays: The same physical setup as Movie 3, but displayed in the embedding space. We see the embedding diagram of the equatorial plane along with the mapped ray trajectories. We see the photons orbit and then climb out of the throat.
