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Dimensional reduction in numerical relativity: Modified cartoon formalism and regularization

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Publication Date: 2016-06-01

Journal Title: International Journal of Modern Physics D

Publisher: World Scientific Publishing Company

Volume: 25

Issue: 9

Number: 1641013

Language: English

Type: Article

Metadata: Show full item record

Citation: Cook, W. G., Figueras, P., Kunesch, M., Sperhake, U., & Tunyasuvunakool, S. (2016). Dimensional reduction in numerical relativity: Modified cartoon formalism and regularization. International Journal of Modern Physics D, 25 (9. 1641013)https://doi.org/10.1142/S0218271816410133

Description: This is the final version of the article. It first appeared from the World Scientific Publishing Company via http://dx.doi.org/10.1142/S0218271816410133

Abstract: 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.

Keywords: black holes, numerical relativity, higher dimensions

Sponsorship: 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 H2020-MSCA-RISE-2015 Grant No. StronGrHEP-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.

Embargo Lift Date: 2100-01-01


External DOI: https://doi.org/10.1142/S0218271816410133

This record's URL: https://www.repository.cam.ac.uk/handle/1810/255731

Rights: Attribution 4.0 International

Licence URL: http://creativecommons.org/licenses/by/4.0/

Author: Cook, William G.Figueras, PauKunesch, MarkusSperhake, UlrichTunyasuvunakool, Saran

Source: https://www.repository.cam.ac.uk/handle/1810/255731


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