Probing the puncture for black hole simulations

Journal Article · Thu Oct 15 04:00:00 EDT 2009 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PHYSREVD.80.084042· OSTI ID:21325386

Brown, J David ^[1]

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1. Department of Physics, North Carolina State University, Raleigh, North Carolina 27695 (United States)

With the puncture method for black hole simulations, the second infinity of a wormhole geometry is compactified to a single 'puncture point' on the computational grid. The region surrounding the puncture quickly evolves to a trumpet geometry. The computational grid covers only a portion of the trumpet throat. It ends at a boundary whose location depends on resolution. This raises the possibility that perturbations in the trumpet geometry could propagate down the trumpet throat, reflect from the puncture boundary, and return to the black hole exterior with a resolution-dependent time delay. Such pathological behavior is not observed. This is explained by the observation that some perturbative modes propagate in the conformal geometry, others propagate in the physical geometry. The puncture boundary exists only in the physical geometry. The modes that propagate in the physical geometry are always directed away from the computational domain at the puncture boundary. The finite difference stencils ensure that these modes are advected through the boundary with no coupling to the modes that propagate in the conformal geometry. These results are supported by numerical experiments with a code that evolves spherically symmetric gravitational fields with standard Cartesian finite difference stencils. The code uses the Baumgarte-Shapiro-Shibata-Nakamura formulation of Einstein's equations with 1+log slicing and gamma-driver shift conditions.

• OSTI ID: 21325386
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 80; ISSN PRVDAQ; ISSN 0556-2821
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BLACK HOLES
COMPACTIFICATION
COUPLING
DISTURBANCES
EINSTEIN FIELD EQUATIONS
GRAVITATIONAL FIELDS
PERTURBATION THEORY
RESOLUTION
SIMULATION
SYMMETRY
TIME DELAY