1+log slicing in gravitational collapse

Ingredients of successful binary black hole simulations Pretorius Generalized harmonic coordinates Excision ____________________________ Campanelli et al and Baker et al BSSN 1+log slicing Gamma freezing shift Moving punctures

Why do these approaches work? BSSN and Harmonic because they make Einstein’s equation look like the wave equation Excision because it gets rid of “grid stretching” 1+log slicing ??? Gamma freezing shift ??? Moving punctures ???

Look at one ingredient at a time 1+log slicing It has been suggested by Rezzolla et al that 1+log slicing and Gamma freezing shift be used in collapse simulations The slicing doesn’t commit you to a particular form of Einstein’s equations

Look at the ingredient in a simple context Spherically symmetric gravitational collapse Scalar field matter Radial length as the spatial coordinate

Maximal slicing Lapse should be small in the middle and approach 1 on the outside to avoid the singularity K=0 D a D a  =[ ] 

Maximal slicing lapse  length

Maximal slicing area radius r length

1+log slicing Elliptic equations take too long to solve, Try something else t  –  i i  = - 2  K This should make  small if K is positive But what if K is negative?

1+log slicing lapse  length

1+log slicing K K length

1+log slicing lapse with excision  length

1+log slicing K with excision K length

Conclusions 1+log slicing is dangerous, use with caution. Use it only with excision 1+log slicing works with moving punctures because moving punctures are “excision without excision”