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Characteristic evolution and matching. (English) Zbl 1166.83300
Summary: I review the development of numerical evolution codes for general relativity based upon the characteristic initial value problem. Progress is traced from the early stage of 1D feasibility studies to 2D axisymmetric codes that accurately simulate the oscillations and gravitational collapse of relativistic stars and to current 3D codes that provide pieces of a binary black hole spacetime. Cauchy codes have now been successful at simulating all aspects of the binary black hole problem inside an artificially constructed outer boundary. A prime application of characteristic evolution is to eliminate the role of this artificial outer boundary via Cauchy-characteristic matching, by which the radiated waveform can be computed at null infinity. Progress in this direction is discussed.
Update of the author’s paper [Zbl 1316.83015], see also the updates [Zbl 1023.83004; Zbl 1316.83016]: Significantly updated previous version. About 30 references have been added. The text has been revised at several points. Added new Sections 4, 5.3 and 6.

MSC:
83-02 Research exposition (monographs, survey articles) pertaining to relativity and gravitational theory
83-08 Computational methods for problems pertaining to relativity and gravitational theory
83C05 Einstein’s equations (general structure, canonical formalism, Cauchy problems)
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