1996/06/06 by Thomas W. Baumgarte, Gregory B. Cook, Mark A. Scheel +3 · 1 citation
Mathematics · Physics and Astronomy · #Algorithm #Applied mathematics #Arithmetic #Astrophysical Phenomena and Observations #Binary number #Black Holes and Theoretical Physics #Black hole (networking) #Coalescence (physics) #Code (set theory) #Computer science #Generalization #Geometry #Horizon #Mathematical analysis #Mathematics #Physics #Pulsars and Gravitational Waves Research #Pure mathematics #Scheme (mathematics) #Set (abstract data type) #TRACE (psycholinguistics) #Tensor (intrinsic definition) #gr-qc
paper · pdf · doi:10.1103/physrevd.54.4849
published as Phys.Rev. D54 (1996) 4849-4857 · 14 pages (RevTeX 3.0 with 3 figures)
arxiv created 1996/06/06 · openalex publication_date 1996/10/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Locating apparent horizons is not only important for a complete understanding of numerically generated spacetimes, but it may also be a crucial component of the technique for evolving black-hole spacetimes accurately. A scheme proposed by Libson, Mass'o, Seidel, and Suen, based on expanding the location of the apparent horizon in terms of symmetric trace-free tensors, seems very promising for use with three-dimensional numerical data sets. In this paper, we generalize this scheme and perform a number of code tests to fully calibrate its behavior in black-hole spacetimes similar to those we expect to encounter in solving the binary black-hole coalescence problem. An important aspect of the generalization is that we can compute the symmetric trace-free tensor expansion to any order. This enables us to determine how far we must carry the expansion to achieve results of a desired accuracy. To accomplish this generalization, we describe a new and very convenient set of recurrence relations which apply to symmetric trace-free tensors.