Three-dimensional initial data for the collision of two black holes

Gregory B. Cook, Matthew W. Choptuik, Mark R. Dubal, Scott Klasky, Richard A. Matzner, and Samuel R. Oliveira
Phys. Rev. D 47, 1471 – Published 15 February 1993
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Abstract

We describe three numerical approaches to the construction of three-dimensional initial data for the collision of two black holes. The first of our approaches involves finite differencing the 3 + 1 Hamiltonian constraint equation on a Čadež coordinate grid. The difference equations are then solved via the multigrid algorithm. The second approach also uses finite-difference techniques, but this time on a regular Cartesian coordinate grid. A Cartesian grid has the advantage of having no coordinate singularities. However, constant coordinate lines are not coincident with the throats of the black holes and, therefore, special treatment of the difference equations at these boundaries is required. The resulting equations are solved using a variant of line-successive overrelaxation. The third and final approach we use is a global, spectral-like method known as the multiquadric approximation scheme. In this case functions are approximated by a finite sum of weighted quadric basis functions which are continuously differentiable. We discuss particular advantages and disadvantages of each method and compare their performances on a set of test problems.

  • Received 31 August 1992

DOI:https://doi.org/10.1103/PhysRevD.47.1471

©1993 American Physical Society

Authors & Affiliations

Gregory B. Cook

  • Center for Radiophysics and Space Research and Center for Theory and Simulation in Science and Engineering, Cornell University, Ithaca, New York 14853

Matthew W. Choptuik and Mark R. Dubal

  • Center for Relativity, University of Texas at Austin, Austin, Texas 78712-1081

Scott Klasky

  • Center for Relativity, University of Texas at Austin, Austin, Texas 78712-1081 and Center for High Performance Computing, University of Texas Systems, Balcones Research Center, 10100 Burnet Rd., Austin, Texas 78758

Richard A. Matzner and Samuel R. Oliveira*

  • Center for Relativity, University of Texas at Austin, Austin, Texas 78712-1081

  • *Present address: Departmento de Fisica, Universidade de Brasilia, Brazil.

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Vol. 47, Iss. 4 — 15 February 1993

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