Towards a stable numerical evolution of strongly gravitating systems in general relativity: The conformal treatments

Miguel Alcubierre, Bernd Brügmann, Thomas Dramlitsch, JoséA A. Font, Philippos Papadopoulos, Edward Seidel, Nikolaos Stergioulas, Ryoji Takahashi

Research output: Contribution to journalArticle

Abstract

We study the stability of three-dimensional numerical evolutions of the Einstein equations, comparing the standard ADM formulation to variations on a family of formulations that separate out the conformal and traceless parts of the system. We develop an implementation of the conformal-traceless (CT) approach that has improved stability properties in evolving weak and strong gravitational fields, and for both vacuum and spacetimes with active coupling to matter sources. Cases studied include weak and strong gravitational wave packets, black holes, boson stars and neutron stars. We show under what conditions the CT approach gives better results in 3D numerical evolutions compared to the ADM formulation. In particular, we show that our implementation of the CT approach gives more long term stable evolutions than ADM in all the cases studied, but is less accurate in the short term for the range of resolutions used in our 3D simulations.

Original languageEnglish (US)
Number of pages1
JournalPhysical Review D - Particles, Fields, Gravitation and Cosmology
Volume62
Issue number4
DOIs
StatePublished - Jan 1 2000

ASJC Scopus subject areas

  • Nuclear and High Energy Physics
  • Physics and Astronomy (miscellaneous)

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