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Accurate black hole evolutions by fourth-order numerical relativity

Y. Zlochower·J. G. Baker·M. Campanelli·C. O. Lousto
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Abstract

We present techniques for successfully performing numerical relativity simulations of binary black holes with fourth-order accuracy. Our simulations are based on a new coding framework which currently supports higher order finite differencing for the BSSN formulation of Einstein's equations, but which is designed to be readily applicable to a broad class of formulations. We apply our techniques to a standard set of numerical relativity test problems, demonstrating the fourth-order accuracy of the solutions. Finally we apply our approach to binary black hole head-on collisions, calculating the waveforms of gravitational radiation generated and demonstrating significant improvements in waveform accuracy over second-order methods with typically achievable numerical resolution.

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Y. Zlochower, J. G. Baker, M. Campanelli, C. O. Lousto. 2005-07-27. Accurate black hole evolutions by fourth-order numerical relativity. https://doi.org/10.1103/physrevd.72.024021

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