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1+log slicing in gravitational collapse

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.

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1+log slicing in gravitational collapse

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  1. 1+log slicingin gravitational collapse

  2. 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

  3. 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 ???

  4. 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

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

  6. Maximal slicing • Lapse should be small in the middle and approach 1 on the outside to avoid the singularity K=0 DaDaa=[ ]a

  7. Maximal slicing lapse a length

  8. Maximal slicing area radius r length

  9. 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?

  10. 1+log slicing lapse a length

  11. 1+log slicing K K length

  12. 1+log slicing lapse with excision a length

  13. 1+log slicing K with excision K length

  14. 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”

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