I am studying the Kerr Metric via the SageMath manifolds module and would like to visualize the casual surfaces generated by light cones. Like the circles in this picture:
Can anybody provide clues about how to program this? SageMath manifolds does provide geodesic ray tracing but I would like the orthogonal surfaces with controls for "elapsed time" (a fluid concept) and off-equatorial angle control for source and slices if 2-d projection is necessary. 3-D would be nice but probably too difficult.
Parametrizing the geodesics, taking orthogonal tangents, and connecting them seems like it would take a long execution time; particularly since I want to watch and control the progress/evolution of the causal boundary.
Suggestions for an alternate forum or Sagemath reference material would be most welcome.