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General relativistic null-cone evolutions with a high-order scheme

Reisswig, Christian and Bishop, Nigel and Pollney, Denis (2013) General relativistic null-cone evolutions with a high-order scheme. General Relativity and Gravitation, 45 (5). pp. 1069-1094. ISSN 0001-7701. doi:10.1007/s10714-013-1513-1.

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We present a high-order scheme for solving the full non-linear Einstein equations on characteristic null hypersurfaces using the framework established by Bondi and Sachs. This formalism allows asymptotically flat spaces to be represented on a finite, compactified grid, and is thus ideal for far-field studies of gravitational radiation. We have designed an algorithm based on 4th-order radial integration and finite differencing, and a spectral representation of angular components. Consequently the scheme offers more accuracy at a given computational cost compared to previous methods which are second-order accurate. Based on a newly implemented code, we show that the new numerical scheme remains stable and is convergent at the expected order of accuracy.

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Additional Information: © 2013 Springer Science+Business Media New York. Received: 22 November 2012; Accepted: 20 February 2013; Published online: 16 March 2013. The authors would like to thank Peter Diener for providing dissipation operator stencil coefficients, and Harald Pfeiffer for comments on the manuscript. We thank the Erwin Schroedinger Institute, Austria, Universitas de les Illes Balears, Spain, and Rhodes University, South Africa, for hospitality. This work is supported by the National Science Foundation under grant numbers AST-0855535 and OCI- 0905046. CR acknowledges support by NASA through Einstein Postdoctoral Fellowship grant number PF2-130099 awarded by the Chandra X-ray center, which is operated by the Smithsonian Astrophysical Observatory for NASA under contract NAS8-03060. NTB has been supported by the National Research Foundation, South Africa. Computations were performed on the LONI network ( under allocation loni_numrel06 and loni_numrel07, and the Caltech compute cluster “Zwicky” (NSF MRI award No. PHY-0960291).
Funding AgencyGrant Number
NASA Einstein Postdoctoral FellowshipPF2-130099
National Research Foundation (South Africa)UNSPECIFIED
NSF MRIPHY-0960291
Subject Keywords:Numerical studies of black holes and black-hole binaries; Wave generation and sources; Gravitational-wave astrophysics; Wave propagation and interactions; Characteristic evolutions
Issue or Number:5
Record Number:CaltechAUTHORS:20130528-090147810
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Official Citation:Reisswig, C., N. Bishop, et al. (2013). "General relativistic null-cone evolutions with a high-order scheme." General Relativity and Gravitation 45(5): 1069-1094.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38679
Deposited By: Tony Diaz
Deposited On:03 Jun 2013 18:36
Last Modified:09 Nov 2021 23:39

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