Cauchy-characteristic extraction in numerical relativity

Nigel T. Bishop, Roberto Gómez, Luis Lehner, and Jeffrey Winicour
Phys. Rev. D 54, 6153 – Published 15 November 1996
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Abstract

We treat the calculation of gravitational radiation using the mixed timelike-null initial value formulation of general relativity. The determination of an exterior radiative solution is based on boundary values on a timelike world tube Γ and on characteristic data on an outgoing null cone emanating from an initial cross section of Γ. We present the details of a three-dimensional computational algorithm which evolves this initial data on a numerical grid, which is compactified to include future null infinity as finite grid points. A code implementing this algorithm is calibrated in the quasispherical regime. We consider the application of this procedure to the extraction of waveforms at infinity from an interior Cauchy evolution, which provides the boundary data on Γ. This is a first step towards Cauchy-characteristic matching in which the data flow at the boundary Γ is two-way, with the Cauchy and characteristic computations providing exact boundary values for each other. We describe strategies for implementing matching and show that for small target error it is much more computationally efficient than alternative methods.

  • Received 17 May 1996

DOI:https://doi.org/10.1103/PhysRevD.54.6153

©1996 American Physical Society

Authors & Affiliations

Nigel T. Bishop

  • Department of Mathematics, Applied Mathematics and Astronomy, University of South Africa, P.O. Box 392, Pretoria 0001, South Africa

Roberto Gómez, Luis Lehner, and Jeffrey Winicour

  • Department of Physics and Astronomy, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

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Vol. 54, Iss. 10 — 15 November 1996

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