Methods to try to solve the Evolution Equations

The inner boundary is a problem for several reasons:

1. We will excise the points inside the apparent horizon.
2. We would like to excise the points inside the event horizon. The problem is that the event horizon is only known at . Thus, we need a way to exclude the singularity of the hole.
3. The apparent horizon is found by looking for Trapped surfaces. This breaks down into solving a very difficult elliptic equation.
4. When the hole moves in the computational domain, coordinate points that were previously excised will now appear inside the computational domain.