140 likes | 279 Views
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.
E N D
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 DaDaa=[ ]a
Maximal slicing lapse a length
Maximal slicing area radius r length
1+log slicing Elliptic equations take too long to solve, Try something else ta – biia = - 2 a K This should make a small if K is positive But what if K is negative?
1+log slicing lapse a length
1+log slicing K K length
1+log slicing lapse with excision a 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”