Exercises to extend the code: level 2

Welcome, kung fu master coder!

You have chosen level 2. The exercises here are as follows:

1. Write new diagnostics to prove that energy is conserved in the time varying spacetime of the scalar field, according to the expressions in Eq. (28) - (31) of this paper.

   The output of this diagnostic will be the (integrated) contributions to Eq. (28), which you can then plot as in Fig 2 for the oscillaton example. (Note that I am deliberately suggesting the normal/Landau-Lifshitz pseudotensor formulation rather than the time-like/Einstein pseudotensor formulation because it is simpler to implement in post processing).

2. Add a spatially constant scalar field to the black hole example (adjust the value of $K$ to make sure you still solve the Hamiltonian constraint initially), and observe the dynamical build up of an accretion cloud, as in this paper. Investigate the effect of changing the scalar mass, recreating the results in Fig. 1.