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- The four dimensional spacetime is split into 3 dimensional hypersurfaces
which evolve in time.
- Breaking spacetime up this way gives us 10 non-linear PDE's to solve
- These equations are divided into two classes.
- 4 Initial Value Equations (Elliptic)
- 6 Coupled Hyperbolic equations (Hyperbolic)
One of the most important components in the solution to the
evolution equation is the choice of gauges.
- The choice of gauge is the choice of coordinate systems.
- Some gauges can allow all the computational grids points to be
``sucked'' inside a black hole, where as other gauge choices can
allow the hole to move on the computational domain.
NOTE:
In Classical Physics evolutions are dictated by momentum variables and
position variables. Numerical Relativity uses the extrinsic curvature, 
to act like the momentum, and the metric 
to act as the position.
The picture below is taken from NCSA. Here again we show the ``pair of
pants''
Scott Klasky
Wed Feb 28 10:19:33 EST 1996