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Numerical Relativity is still Relativity

Numerical Relativity is still Relativity. ERE Salamanca 2008 Palma Group Alic, Dana · Bona, Carles · Bona-Casas, Carles. Most recent successful stories in BH simulations. Long term evolutions: Harmonic (4D spacetime, excision, harmonic gauge source functions)

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Numerical Relativity is still Relativity

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

  2. Most recent successful stories in BH simulations • 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?

  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) • 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=30 t=1000

  8. t=1000; Amplitude 0.5

  9. Single BH Test • Singularity avoidant conditions (Bona-Massó) 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.

  13. Shift • 1st order conditions. • Vectorial. • Harmonic?  xi = 0. 1st order version

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

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

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