Click here to download the worksheet file (ipynb format). To run it, you must start SageMath with the Jupyter notebook, with the command sage -n jupyter
First we set up the notebook to display mathematical objects using LaTeX formatting:
We declare the spacetime manifold M:
4-dimensional differentiable manifold M
We use coordinates (t,r,θ,ϕ) analogous to the 3+1 Eddington-Finkelstein coordinates in Schwarzschild spacetime, i.e. coordinates such that the advanced time v=t+r is constant on the ingoing radial null geodesics:
A zoom on the trapping horizon in its dynamical part: notice that the "outgoing" null geodesics cross it with a vertical tangent, in agreement with the cross-sections of the trapping horizon being marginally trapped surfaces.