2005/09/22 by C. Bona, Carles Bona, Luis Lehner +2 · 20 citations
Engineering · Mathematics · Physics and Astronomy · #Applied mathematics #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Boundary (topology) #Boundary value problem #Computer science #Coordinate system #Elliptic coordinate system #Engineering #Gauge (firearms) #Geometry #Mathematical analysis #Mathematics #Metric (unit) #Outflow #Physics #Pulsars and Gravitational Waves Research #Scalar (mathematics) #gr-qc
paper · pdf · doi:10.1103/physrevd.72.104009
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 72(10) (American Physical Society) · 9 figures
arxiv created 2005/09/22 · openalex publication_date 2005/11/14 · arxiv updated 2011/04/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We study the implications of adopting hyperbolic-driver coordinate conditions motivated by geometrical considerations. In particular, conditions that minimize the rate of change of the metric variables. We analyze the properties of the resulting system of equations and their effect when implementing excision techniques. We find that commonly used coordinate conditions lead to a characteristic structure at the excision surface where some modes are not of outflow type with respect to any excision boundary chosen inside the horizon. Thus, boundary conditions are required for these modes. Unfortunately, the specification of these conditions is a delicate issue as the outflow modes involve both gauge and main variables. As an alternative to these driver equations, we examine conditions derived from extremizing a scalar constructed from Killing's equation and present specific numerical examples.