Dimensional reduction in numerical relativity: Modified Cartoon formalism and regularization
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.
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.Attached Files
Published - s0218271816410133.pdf
Submitted - 1603.00362v1.pdf
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Additional details
- Eprint ID
- 70256
- Resolver ID
- CaltechAUTHORS:20160909-141302514
- MaGRaTh-646597
- European Research Council (ERC)
- 690904
- Marie Curie Fellowship
- ST/L000636/1
- Science and Technology Facilities Council (STFC)
- PHY-090003
- NSF
- Higher Education Funding Council for England
- ST/J005673/1
- Science and Technology Facilities Council (STFC)
- ST/H008586/1
- Science and Technology Facilities Council (STFC)
- ST/K00333X/1
- Science and Technology Facilities Council (STFC)
- NewNGR-639022
- European Research Council (ERC)
- Royal Society
- Created
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2016-09-12Created from EPrint's datestamp field
- Updated
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2021-11-11Created from EPrint's last_modified field