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Classifying the isolated zeros of asymptotic gravitational radiation by tendex and vortex lines

Zimmerman, Aaron and Nichols, David A. and Zhang, Fan (2011) Classifying the isolated zeros of asymptotic gravitational radiation by tendex and vortex lines. Physical Review D, 84 (4). Art. No. 044037. ISSN 0556-2821.

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A new method to visualize the curvature of spacetime was recently proposed. This method finds the eigenvectors of the electric and magnetic components of the Weyl tensor and, in analogy to the field lines of electromagnetism, uses the eigenvectors’ integral curves to illustrate the spacetime curvature. Here we use this approach, along with well-known topological properties of fields on closed surfaces, to show that an arbitrary, radiating, asymptotically flat spacetime must have points near null infinity where the gravitational radiation vanishes. At the zeros of the gravitational radiation, the field of integral curves develops singular features analogous to the critical points of a vector field. We can, therefore, apply the topological classification of singular points of unoriented lines as a method to describe the radiation field. We provide examples of the structure of these points using linearized gravity and discuss an application to the extreme-kick black-hole-binary merger.

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Additional Information:© 2011 American Physical Society. Received 14 July 2011; published 11 August 2011. We thank Rob Owen for inspiring our investigation of ridge topology in tendex and vortex patterns. We would also like to thank Yanbei Chen, Tanja Hinderer, Jeffrey D. Kaplan, Geoffrey Lovelace, Charles W. Misner, Ezra T. Newman, and Kip S. Thorne for valuable discussions. This research was supported by NSF Grants No. PHY-0601459, PHY-0653653, PHY-1005655, CAREER Grant PHY-0956189, NASA Grant No. NNX09AF97G, the Sherman Fairchild Foundation, the Brinson Foundation, and the David and Barabara Groce Startup Fund.
Funding AgencyGrant Number
Sherman Fairchild Foundation UNSPECIFIED
Brinson Foundation UNSPECIFIED
David and Barabara Groce Startup FundUNSPECIFIED
Classification Code:PACS: 04.30.-w, 02.40.Pc, 04.20.-q
Record Number:CaltechAUTHORS:20110829-131730400
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:25149
Deposited By: Tony Diaz
Deposited On:30 Aug 2011 15:26
Last Modified:26 Dec 2012 13:38

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