General relativistic null-cone evolutions with a high-order scheme |
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Authors: | Christian Reisswig Nigel Bishop Denis Pollney |
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Affiliation: | 1. Theoretical Astrophysics Including Relativity, California Institute of Technology, Pasadena, CA, 91125, USA 2. Department of Mathematics, Rhodes University, Grahamstown, 6139, South Africa
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Abstract: | 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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