3:Casual differencing
Evolve only the exterior of the hole, ignore interior.
- No boundary condition should be imposed at the horizon.
Coordinates are well-behaved:
- Coordinates do not fall into a stationary hole
- Hole is allowed to move through the grid.
- Requires large shift vector: difficult in computations.
Using CD, quantities are evolved along the center of the local light cone, then placed at their spatial locations.
Casual differencing allows for arbitrary choice of shift vector, makes the courant condition independent of the shift, naturally handles black hole excision, moving holes.