Finite difference schemes for second order systems describing black holes

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In the harmonic description of general relativity, the principal part of Einstein’s equations reduces to 10 curved space wave equations for the components of the space-time metric. We present theorems regarding the stability of several evolution-boundary algorithms for such equations when treated in second order differential form. The theorems apply to a model black hole space-time consisting of a spacelike inner boundary excising the singularity, a timelike outer boundary and a horizon in between. These algorithms are implemented as stable, convergent numerical codes and their performance is compared in a 2-dimensional excision problem.


The preprint is available from arXiv at: http://arxiv.org/pdf/gr-qc/0604010v1.pdf. The citation for the preprint is Motamed, M., Babiuc, M., Szilagyi, B., Kreiss, H. O., & Winicour, J. (2006). Finite difference schemes for second order systems describing black holes. arXiv preprint gr-qc/0604010.

The version of record is available from the American Physical Society at http://dx.doi.org/10.1103/PhysRevD.73.124008.

© 2006 The American Physical Society. All rights reserved.