Numerical Challenges in Simulating Spacetime
Coordinate freedom — because we are trying to solve for the structure of spacetime, coordinates are merely labels, and do not, a priori, have any geometric significance. A poor choice of coordinates can lead to coordinate singularities, and hence code crashes.
Singularity avoidance — black holes contain physical singularities that must be “avoided”
- use a singularity-avoiding slicing condition (plagued by “grid-stretching”)
- black hole excision