SageMath notebooks associated to the Black Hole Lectures (https://luth.obspm.fr/~luthier/gourgoulhon/bh16)
Plot of principal null geodesics in Kerr spacetime
This Jupyter/SageMath notebook is relative to the lectures Geometry and physics of black holes.
The computations make use of tools developed through the SageManifolds project.
First we set up the notebook to display mathematical objects using LaTeX rendering:
Spacetime manifold
We declare the Kerr spacetime as a 4-dimensional Lorentzian manifold :
and introduce the (3+1 version of) Kerr coordinates as a chart KC
on , via the method chart()
. The argument of the latter is a string (delimited by r"..."
because of the backslash symbols) expressing the coordinates names, their ranges (the default is ) and their LaTeX symbols:
Plot of the principal null geodesics in the plane
Adding the vectors and to the plot
We add the vectors and at the intersection of the ingoing geodesic with the outgoing one: