Probing the puncture for black hole simulations - General Relativity and Quantum CosmologyReport as inadecuate

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Abstract: With the puncture method for black hole simulations, the second infinity of awormhole geometry is compactified to a single -puncture point- on thecomputational grid. The region surrounding the puncture quickly evolves to atrumpet geometry. The computational grid covers only a portion of the trumpetthroat. It ends at a boundary whose location depends on resolution. This raisesthe possibility that perturbations in the trumpet geometry could propagate downthe trumpet throat, reflect from the puncture boundary, and return to the blackhole exterior with a resolution-dependent time delay. Such pathologicalbehavior is not observed. This is explained by the observation that someperturbative modes propagate in the conformal geometry, others propagate in thephysical geometry. The puncture boundary exists only in the physical geometry.The modes that propagate in the physical geometry are always directed away fromthe computational domain at the puncture boundary. The finite differencestencils ensure that these modes are advected through the boundary with nocoupling to the modes that propagate in the conformal geometry. These resultsare supported by numerical experiments with a code that evolves sphericallysymmetric gravitational fields with standard Cartesian finite differencestencils. The code uses the Baumgarte-Shapiro-Shibata-Nakamura formulationof Einstein-s equations with 1+log slicing and gamma-driver shift conditions.

Author: J. David Brown



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