2001/03/27 by Bernard Kelly, Pablo Laguna, Keith Lockitch +5 · 29 citations
Mathematics · Physics and Astronomy · #Applied mathematics #Black Holes and Theoretical Physics #Black hole (networking) #Circular symmetry #Classical mechanics #Computer science #Constraint (computer-aided design) #Cosmology and Gravitation Theories #Einstein #Geometry #Gravitation #Gravitational singularity #Mathematical analysis #Mathematics #Numerical relativity #Physics #Pulsars and Gravitational Waves Research #Quantum mechanics #Space (punctuation) #Spacetime #Stability (learning theory) #Symmetry (geometry) #Term (time) #gr-qc
paper · pdf · doi:10.1103/physrevd.64.084013
published in Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields 64(8) (American Physical Society) · 20 pages, 9 figures
arxiv created 2001/03/27 · openalex publication_date 2001/09/01 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Numerical codes based on a direct implementation of the standard Arnowitt-Deser-Misner (ADM) formulation of Einstein's equations have generally failed to provide long-term stable and convergent evolutions of black hole space-times when excision is used to remove the singularities. We show that, for the case of a single black hole in spherical symmetry, it is possible to circumvent these problems by adding terms involving the constraints to the evolution equations, thus adjusting the standard ADM system. We investigate the effect that the choice of the lapse and shift has on the stability properties of numerical simulations and thus on the form of the added constraint term. To facilitate this task, we introduce the concept of quasi-well-posedness, a version of well-posedness suitable for ADM-like systems involving second-order spatial derivatives.