Workshop From geometry to numerics
IHP, Paris, 20-24 November 2006

Niall O' Murchadha (Cork Univ., Ireland)

Excision without excision: why the puncture method works

The successful Brownsville and Goddard binary black hole codes have much in common. Both use puncture data and evolve using BSSN. As a slicing condition they use `1 + log' to pick the lapse and `gamma-freezing' to fix the shift. The Jena group tried to evolve the Schwarzschild solution using exactly these choices. The outcome was surprising. The lapse collapsed `at the puncture' and the slice evolved to a stationary state. This stationary state was asymptotically flat at one end and cylindrical at the other, of radius R = 1.31 M. What happened is that the code took all the grid points `near the puncture'(in the left quadrant of the extended Schwarzschild) and dragged them to the right so that they ended up in the upper quadrant, on the cylinder of areal radius 1.3. M. Thus the code excised the puncture and replaced it with a much smoother cylinder. We conjecture that this is why the puncture method works so well in the binary black hole problem.

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