1. Numerical Relativity is still Relativity ERE Salamanca 2008 Palma Group Alic, Dana · Bona, Carles · Bona-Casas, Carles

2. Long term evolutions: –Harmonic (4D spacetime, excision, harmonic gauge source functions) –BSSN (3+1 decomposition, punctures/excision, 1+log and gamma freezing) Isn ’ t the gauge choice too limited? Shouldn ’ t numerical relativity be relativity? Most recent successful stories in BH simulations

3. Do we have any choice? Reported experiences: –No long term simulations with normal coordinates (zero shift). –Generalised harmonic slicing but strictly harmonic shift. –BSSN normal coordinates (zero shift) and 1+log slicing crashes at 30-40M ( gr-qc/0206072 ). –Gaugewave test: gauge imposed is harmonic, so harmonic code succeeds, but BSSN crashes.

4. Looking for a gauge polyvalent code Z4 formalism MoL with 3rd order SSP Runge-Kutta. Powerful 3rd order FD algorithm (submitted to JCP). See a variant in http://arxiv.org/abs/0711.4685 (ERE 2007) http://arxiv.org/abs/0711.4685 Scalar field stuffing. Cactus. Single grid calculation. Logarithmic grid for long runs.

5. Gaugewave Test Minkowski spacetime: Harmonic coordinates x,y,z,t.

6. t=1000; Amplitude 0.1

7. BSSN Comparison t=1000 t=30

8. t=1000; Amplitude 0.5

9. Single BH Test Singularity avoidant conditions (Bona-Mass ó ) Q = f (trK-2  ) 1+log (f=2/  ) slicing with normal coordinates (zero shift) up to 1000M and more! Never done before (BSSN reported to crash at 30- 40M without shift). Unigrid simulation. Logcoords =1.5.

10. Lapse function at t=1000M

11. R/M=20 r/M=463000

12. More gauges (zero shift) Isotropic coords. Boundaries at 20M. Logcoords f=1/  150M. Slicing (f) 2/  1+1/  1/2+1/  1/  1/4+3/4  1/2+1/2  Vol. Elem. left 37%25%20%14%10%6% Time lasting (0.2 / 0.1 resol) 50M / 50M / 50M / 50M 6M / 50M 6M / 20M 5M / 12M

13. Shift 1st order conditions. Vectorial. –Harmonic?  x i = 0. 1st order version

14. Advection terms Lie derivative “ advection/damping ” Covariant advection term

15. 1st order vector ingredients Time-independent coordinate transformations.