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.
@article{arxiv.gr-qc/0505055,
title = {Accurate black hole evolutions by fourth-order numerical relativity},
author = {Y. Zlochower and J. G. Baker and M. Campanelli and C. O. Lousto},
journal= {arXiv preprint arXiv:gr-qc/0505055},
year = {2009}
}