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Dimensional reduction in numerical relativity: Modified Cartoon formalism and regularization

Cook, William G. and Figueras, Pau and Kunesch, Markus and Sperhake, Ulrich and Tunyasuvunakool, Saran (2016) Dimensional reduction in numerical relativity: Modified Cartoon formalism and regularization. International Journal of Modern Physics D, 25 (9). Art. No. 1641013. ISSN 0218-2718. doi:10.1142/S0218271816410133.

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We present in detail the Einstein equations in the Baumgarte–Shapiro–Shibata–Nakamura formulation for the case of D-dimensional spacetimes with SO(D−d) isometry based on a method originally introduced in Ref. 1. Regularized expressions are given for a numerical implementation of this method on a vertex centered grid including the origin of the quasi-radial coordinate that covers the extra dimensions with rotational symmetry. Axisymmetry, corresponding to the value d=D−2, represents a special case with fewer constraints on the vanishing of tensor components and is conveniently implemented in a variation of the general method. The robustness of the scheme is demonstrated for the case of a black-hole head-on collision in D=7 spacetime dimensions with SO(4) symmetry.

Item Type:Article
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URLURL TypeDescription Paper
Sperhake, Ulrich0000-0002-3134-7088
Additional Information:© 2016 The Authors. This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC-BY) License. Further distribution of this work is permitted, provided the original work is properly cited. Received: 29 February 2016; Revised: 11 April 2016; Accepted: 28 April 2016; Published: 1 June 2016. U.S. is supported by the H2020 ERC Consolidator Grant “Matter and strong-field gravity: New frontiers in Einstein’s theory” grant agreement No. MaGRaTh–646597, the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No. 690904, the STFC Consolidator Grant No. ST/L000636/1, the SDSC Comet 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. P.F. and S.T. are supported by the H2020 ERC Starting Grant “New frontiers in numerical general relativity” grant agreement No. NewNGR-639022. P.F. is also supported by a Royal Society University Research Fellowship. W.G.C. and M.K. are supported by STFC studentships.
Funding AgencyGrant Number
European Research Council (ERC)MaGRaTh-646597
Marie Curie Fellowship690904
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
European Research Council (ERC)NewNGR-639022
Subject Keywords:Black holes; numerical relativity; higher dimensions
Issue or Number:9
Classification Code:PACS: 04.25.D−, 04.70.−s, 04.50.−h, 04.25.dg
Record Number:CaltechAUTHORS:20160909-141302514
Persistent URL:
Official Citation:William G. Cook et al, Int. J. Mod. Phys. D 25, 1641013 (2016) [27 pages] DOI:
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:70256
Deposited By: Tony Diaz
Deposited On:12 Sep 2016 19:00
Last Modified:11 Nov 2021 04:26

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