Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model

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Acknowledgement

We thank Misha Ivanov, Rafael Porto, Zihan Zhou for useful discussion. We are especially grateful to Thibault Damour for detailed discussions on the mass polynomiality of the impulse. We would also like to thank Benjamin Leather for providing the code used to generate Fig. 1. This research was supported in part by the U.S. Department of Energy (DOE) under Grants No. DE-SC0009937, No. DE-SC00019066, No. DE-SC0011632 and No. DE-SC0009919 and in part by the U.S. National Science Foundation under Grant No. NSF PHY-1748958. In relation to the latter support, we thank the Kavli Institute for Theoretical Physics for their hospitality, where this paper was initiated. M. Z.'s work is supported in part by the U.K. Royal Society through Grant No. URF\R1\20109. J. P.-M. would like to thank the Institut des Hautes Études Scientifiques and the Korea Institute for Advanced Study, for their hospitality while this work was being completed. M. P. S. is supported by the Alfred P. Sloan Foundation. We are also grateful to the Mani L. Bhaumik Institute for Theoretical Physics and the Walter Burke Institute for Theoretical Physics for support. We acknowledge the use of the IRIDIS High-Performance Computing Facility, and associated support services at the University of Southampton, in the completion of this work. This work makes use of the Black Hole Perturbation Toolkit [143].