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General relativistic null-cone evolutions with a high-order scheme. (English) Zbl 1269.83014
Summary: 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.

MSC:
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
83C57 Black holes
83-08 Computational methods for problems pertaining to relativity and gravitational theory
85A25 Radiative transfer in astronomy and astrophysics
83C35 Gravitational waves
83C25 Approximation procedures, weak fields in general relativity and gravitational theory
85A04 General questions in astronomy and astrophysics
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