Stability of the puncture method with a generalized Baumgarte-Shapiro-Shibata-Nakamura formulation

Helvi Witek, David Hilditch, and Ulrich Sperhake
Phys. Rev. D 83, 104041 – Published 20 May 2011

Abstract

The puncture method for dealing with black holes in the numerical simulation of vacuum spacetimes is remarkably successful when combined with the Baumgarte-Shapiro-Shibata-Nakamura (BSSN) formulation of the Einstein equations. We examine a generalized class of formulations modeled along the lines of the Laguna-Shoemaker system and including BSSN as a special case. The formulation is a two parameter generalization of the choice of variables used in standard BSSN evolutions. Numerical stability of the standard finite difference methods is proven for the formulation in the linear regime around flat space, a special case of which is the numerical stability of BSSN. Numerical evolutions are presented and compared with a standard BSSN implementation. Surprisingly, a significant portion of the parameter space yields (long-term) stable simulations, including the standard BSSN formulation as a special case. Furthermore, nonstandard parameter choices typically result in smoother behavior of the evolution variables close to the puncture.

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  • Received 22 November 2010

DOI:https://doi.org/10.1103/PhysRevD.83.104041

© 2011 American Physical Society

Authors & Affiliations

Helvi Witek1,2,*, David Hilditch2,†, and Ulrich Sperhake2,3,4,5,‡

  • 1Centro Multidisciplinar de Astrofísica—CENTRA, Departamento de Física, Instituto Superior Técnico—IST, Universidade Técnica de Lisboa - UTL, Av. Rovisco Pais 1, 1049-001 Lisboa, Portugal
  • 2Theoretisch-Physikalisches Institut, Friedrich-Schiller Universität Jena, Max-Wien Platz 1, 07743 Jena, Germany
  • 3Institut de Ciències de l’Espai (CSIC-IEEC), Facultat de Ciències, Campus UAB, E-08193 Bellaterra, Spain
  • 4Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, California 91125, USA
  • 5Department of Physics and Astronomy, The University of Mississippi, University, Mississippi 38677, USA

  • *helvi.witek@ist.utl.pt
  • david.hilditch@uni-jena.de
  • sperhake@tapir.caltech.edu

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Vol. 83, Iss. 10 — 15 May 2011

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