Zhang, Fan and Brink, Jeandrew and Szilágyi, Béla and Lovelace, Geoffrey (2012) Geometrically motivated coordinate system for exploring spacetime dynamics in numerical-relativity simulations using a quasi-Kinnersley tetrad. Physical Review D, 86 (8). Art. No. 084020. ISSN 0556-2821. http://resolver.caltech.edu/CaltechAUTHORS:20121101-143332978
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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.
|Additional Information:||© 2012 American Physical Society. Received 2 August 2012; published 3 October 2012. We would like to thank Luisa Buchmann for alerting the NR group at Caltech about the potential of the QKTs to aid wave extraction, and we are indebted to Andrea Nerozzi and Rob Owen for many useful discussions and to Mark Scheel for numerous assistance with the SpEC code. This research was supported by NSF Grants No. PHY-1068881 and No. PHY-1005655 at Caltech and by NSF Grants No. PHY-0969111, No. PHY-1005426 at Cornell, by NASA Grants No. NNX09AF97G and No. NNX09AF96G, and by the Sherman Fairchild Foundation to Caltech and Cornell and the Brinson Foundation to Caltech. The numerical computations in this paper were completed using the Caltech computer cluster ZWICKY, which was funded by the Sherman Fairchild Foundation and the NSF MRI-R2 Grant No. PHY-0960291 to Caltech.|
|Classification Code:||PACS: 04.25.D-, 04.30.-w, 04.25.dg|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||01 Nov 2012 21:44|
|Last Modified:||27 Dec 2012 02:57|
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