# Brill Waves

### From GRwiki

## Brill Waves

This is not actually a single analytic solution to the field equations in itself, but rather a method for numerically solving for the behavior of the metric given initial conditions on an azymuthally symmetric metric. You start out with a metric which has a constant time slice of

where the behavior is restricted to

- goes to zero faster than where

You start out with your choice of metric initially satisfying these equations, then by computer numerically time step the metric elements by so that the variation in the elements accord with Einstein's field equations. You then look at how a computer simulation describes the time dependent metric. Such simulations indicate that colliding gravitational waves can collapse to form a black hole.

## References

[1]*Relativity - equations 9.3.18-9.3.19