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Extraction of gravitational-wave energy in higher dimensional numerical relativity using the Weyl tensor

Cook, William G. and Sperhake, Ulrich (2017) Extraction of gravitational-wave energy in higher dimensional numerical relativity using the Weyl tensor. Classical and Quantum Gravity, 34 (3). Art. No. 035010. ISSN 0264-9381. doi:10.1088/1361-6382/aa5294.

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Gravitational waves are one of the most important diagnostic tools in the analysis of strong-gravity dynamics and have been turned into an observational channel with LIGO's detection of GW150914. Aside from their importance in astrophysics, black holes and compact matter distributions have also assumed a central role in many other branches of physics. These applications often involve spacetimes with D  >  4 dimensions where the calculation of gravitational waves is more involved than in the four dimensional case, but has now become possible thanks to substantial progress in the theoretical study of general relativity in D  >  4. Here, we develop a numerical implementation of the formalism by Godazgar and Reall [1]—based on projections of the Weyl tensor analogous to the Newman–Penrose scalars—that allows for the calculation of gravitational waves in higher dimensional spacetimes with rotational symmetry. We apply and test this method in black-hole head-on collisions from rest in D  =  6 spacetime dimensions and find that a fraction (8.19 ± 0.05) ± {10^(-4) of the Arnowitt–Deser–Misner mass is radiated away from the system, in excellent agreement with literature results based on the Kodama–Ishibashi perturbation technique. The method presented here complements the perturbative approach by automatically including contributions from all multipoles rather than computing the energy content of individual multipoles.

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Sperhake, Ulrich0000-0002-3134-7088
Additional Information:© 2017 IOP Publishing Ltd. Original content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. Received 2 September 2016, revised 10 November 2016. Accepted for publication 8 December 2016. Published 9 January 2017. We thank Pau Figueras, Mahdi Godazgar, Markus Kunesch, Harvey Reall, Saran Tunyasuvunakool and Helvi Witek for highly fruitful discussions of this topic. This work has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie SkŁodowska-Curie grant agreement No 690904, from H2020-ERC-2014-CoG Grant No. 'MaGRaTh' 646597, from STFC Consolidator Grant No. ST/L000636/1, the SDSC Comet, PSC-Bridges and TACC Stampede clusters through NSF-XSEDE Award Nos. PHY-090003, the Cambridge High Performance Computing Service Supercomputer Darwin using Strategic Research Infrastructure Funding from the HEFCE and the STFC, and DiRAC's Cosmos Shared Memory system through BIS Grant No. ST/J005673/1 and STFC Grant Nos. ST/H008586/1, ST/K00333X/1. WGC is supported by a STFC studentship.
Funding AgencyGrant Number
Marie Curie Fellowship690904
European Research Council (ERC)MaGRaTh 646597
Science and Technology Facilities Council (STFC)ST/L000636/1
Higher Education Funding Council for EnglandUNSPECIFIED
Science and Technology Facilities Council (STFC)ST/J005673/1
Science and Technology Facilities Council (STFC)ST/H008586/1
Science and Technology Facilities Council (STFC)ST/K00333X/1
Issue or Number:3
Record Number:CaltechAUTHORS:20170110-111519979
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Official Citation:William G Cook and Ulrich Sperhake 2017 Class. Quantum Grav. 34 035010
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:73371
Deposited By: George Porter
Deposited On:10 Jan 2017 20:39
Last Modified:11 Nov 2021 05:15

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