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Towards a wave-extraction method for numerical relativity. II. The quasi-Kinnersley frame

Andrea Nerozzi1,2, Christopher Beetle3,4, Marco Bruni1, Lior M. Burko3,5, and Denis Pollney6

  • 1Institute of Cosmology and Gravitation, University of Portsmouth, Portsmouth PO1 2EG, United Kingdom
  • 2Center for Relativity, Department of Physics, University of Texas at Austin, Austin, Texas 78712-1081, USA
  • 3Department of Physics, University of Utah, Salt Lake City, Utah 84112, USA
  • 4Department of Physics, Florida Atlantic University, Boca Raton, Florida 33431, USA
  • 5Department of Physics and Astronomy, Bates College, Lewiston, Maine 04240, USA
  • 6Max-Planck-Institut für Gravitationsphysik, Albert-Einstein-Institut, 14476 Golm, Germany

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Phys. Rev. D 72, 024014 – Published 15 July, 2005

DOI: https://doi.org/10.1103/PhysRevD.72.024014

Abstract

The Newman-Penrose formalism may be used in numerical relativity to extract coordinate-invariant information about gravitational radiation emitted in strong-field dynamical scenarios. The main challenge in doing so is to identify a null tetrad appropriately adapted to the simulated geometry such that Newman-Penrose quantities computed relative to it have an invariant physical meaning. In black hole perturbation theory, the Teukolsky formalism uses such adapted tetrads, those which differ only perturbatively from the background Kinnersley tetrad. At late times, numerical simulations of astrophysical processes producing isolated black holes ought to admit descriptions in the Teukolsky formalism. However, adapted tetrads in this context must be identified using only the numerically computed metric, since no background Kerr geometry is known a priori. To do this, this paper introduces the notion of a quasi-Kinnersley frame. This frame, when space-time is perturbatively close to Kerr, approximates the background Kinnersley frame. However, it remains calculable much more generally, in space-times nonperturbatively different from Kerr. We give an explicit solution for the tetrad transformation which is required in order to find this frame in a general space-time.

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Towards a wave-extraction method for numerical relativity. I. Foundations and initial-value formulation

Christopher Beetle, Marco Bruni, Lior M. Burko, and Andrea Nerozzi
Phys. Rev. D 72, 024013 (2005)

Article Text

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Outline

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Phys. Rev. D 72, 024014– Published 15 July, 2005
  • Received 5 July 2004

© 2005 American Physical Society

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