Abstract
We obtain a fourth-order accurate numerical algorithm to integrate the Zerilli and Regge–Wheeler wave equations, describing perturbations of non-rotating black holes, with source terms due to an orbiting particle. Those source terms contain Dirac's delta and its first derivative. We also re-derive the source of the Zerilli and Regge–Wheeler equations for more convenient definitions of the waveforms that allow direct metric reconstruction (in the Regge–Wheeler gauge).
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