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Finite Difference Schemes For Second Order Systems Describing Black Holes, Mohammad Motamed, Maria Babiuc-Hamilton, B. Szilágyi, H-O. Kreiss, J. Winicour
Finite Difference Schemes For Second Order Systems Describing Black Holes, Mohammad Motamed, Maria Babiuc-Hamilton, B. Szilágyi, H-O. Kreiss, J. Winicour
Maria Babiuc-Hamilton
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.