Geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad

Fan Zhang, Jeandrew Brink, Béla Szilágyi, and Geoffrey Lovelace
Phys. Rev. D 86, 084020 – Published 3 October 2012

Abstract

We investigate the suitability and properties of a quasi-Kinnersley tetrad and a geometrically motivated coordinate system as tools for quantifying both strong-field and wave-zone effects in numerical relativity (NR) simulations. We fix two of the coordinate degrees of freedom of the metric, namely, the radial and latitudinal coordinates, using the Coulomb potential associated with the quasi-Kinnersley transverse frame. These coordinates are invariants of the spacetime and can be used to unambiguously fix the outstanding spin-boost freedom associated with the quasi-Kinnersley frame (and thus can be used to choose a preferred quasi-Kinnersley tetrad). In the limit of small perturbations about a Kerr spacetime, these geometrically motivated coordinates and quasi-Kinnersley tetrad reduce to Boyer-Lindquist coordinates and the Kinnersley tetrad, irrespective of the simulation gauge choice. We explore the properties of this construction both analytically and numerically, and we gain insights regarding the propagation of radiation described by a super-Poynting vector, further motivating the use of this construction in NR simulations. We also quantify in detail the peeling properties of the chosen tetrad and gauge. We argue that these choices are particularly well-suited for a rapidly converging wave-extraction algorithm as the extraction location approaches infinity, and we explore numerically the extent to which this property remains applicable on the interior of a computational domain. Using a number of additional tests, we verify numerically that the prescription behaves as required in the appropriate limits regardless of simulation gauge; these tests could also serve to benchmark other wave extraction methods. We explore the behavior of the geometrically motivated coordinate system in dynamical binary-black-hole NR mergers; while we obtain no unexpected results, we do find that these coordinates turn out to be useful for visualizing NR simulations (for example, for vividly illustrating effects such as the initial burst of spurious junk radiation passing through the computational domain). Finally, we carefully scrutinize the head-on collision of two black holes and, for example, the way in which the extracted waveform changes as it moves through the computational domain.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
10 More
  • Received 2 August 2012

DOI:https://doi.org/10.1103/PhysRevD.86.084020

© 2012 American Physical Society

Authors & Affiliations

Fan Zhang1, Jeandrew Brink2, Béla Szilágyi1, and Geoffrey Lovelace3

  • 1Theoretical Astrophysics 350-17, California Institute of Technology, Pasadena, California 91125, USA
  • 2National Institute of Theoretical Physics, Private Bag X1 Matieland, Stellenbosch 7602, South Africa
  • 3Center for Radiophysics and Space Research, Cornell University, Ithaca, New York 14853, USA

Article Text (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 86, Iss. 8 — 15 October 2012

Reuse & Permissions
Access Options
CHORUS

Article Available via CHORUS

Download Accepted Manuscript
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×