Numerical Relativity is still Relativity

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Numerical Relativity is still Relativity

• ERE Salamanca 2008
• Palma Group
• Alic, Dana Bona, Carles Bona-Casas, Carles

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Most recent successful stories in BH simulations

• Long term evolutions
• Harmonic (4D spacetime, excision, harmonic gauge
  source functions)
• BSSN (31 decomposition, punctures/excision,
  1log and gamma freezing)
• Isnt the gauge choice too limited? Shouldnt
  numerical relativity be relativity?

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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 1log
  slicing crashes at 30-40M (gr-qc/0206072).
• Gaugewave test gauge imposed is harmonic, so
  harmonic code succeeds, but BSSN crashes.

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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/0711.4
  685 (ERE 2007)
• Scalar field stuffing.
• Cactus. Single grid calculation. Logarithmic grid
  for long runs.

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Gaugewave Test

• Minkowski spacetime
• Harmonic coordinates x,y,z,t.

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t1000 Amplitude 0.1
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BSSN Comparison
t1000

• t30

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t1000 Amplitude 0.5
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Single BH Test

• Singularity avoidant conditions (Bona-Massó)
• Q f (trK-2?)
• 1log (f2/?) 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.

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Lapse function at t1000M
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R/M20 r/M463000
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More gauges (zero shift)

• Isotropic coords. Boundaries at 20M.
• Logcoords f1/? 150M.

Slicing (f) 2/? 11/? 1/21/? 1/? 1/43/4? 1/21/2?
Vol. Elem. left 37 25 20 14 10 6
Time lasting (0.2 / 0.1 resol) 50M / 50M 50M / 50M 50M / 50M 6M / 50M 6M / 20M 5M/12M
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Shift

• 1st order conditions.
• Vectorial.
• Harmonic? ? xi 0.

1st order version
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Advection terms

• Lie derivative advection/damping
• Covariant advection term

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1st order vector ingredients

• Time-independent coordinate transformations.

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