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arXiv · 2304.09200

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

Leor Barack·Zvi Bern·Enrico Herrmann·Oliver Long·Julio Parra-Martinez·Radu Roiban·Michael S. Ruf·Chia-Hsien Shen·Mikhail P. Solon·Fei Teng·Mao Zeng
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Abstract

We compare numerical self-force results and analytical fourth-order post-Minkowskian (PM) calculations for hyperbolic-type scattering of a point-like particle carrying a scalar charge $Q$ off a Schwarzschild black hole, showing a remarkably good agreement. Specifically, we numerically compute the scattering angle including the full $O(Q^2)$ scalar-field self-force term (but ignoring the gravitational self-force), and compare with analytical expressions obtained in a PM framework using scattering-amplitude methods. This example provides a nontrivial, high-precision test of both calculation methods, and illustrates the complementarity of the two approaches in the context of the program to provide high-precision models of gravitational two-body dynamics. Our PM calculation is carried out through 4PM order, i.e., including all terms through $O(Q^2 G^3)$. At the fourth post-Minkowskian order the point-particle description involves two a-priori undetermined coefficients, due to contributions from tidal effects in the model under consideration. These coefficients are chosen to align the post-Minkowskian results with the self-force ones.

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Leor Barack, Zvi Bern, Enrico Herrmann, Oliver Long, Julio Parra-Martinez, Radu Roiban, Michael S. Ruf, Chia-Hsien Shen, Mikhail P. Solon, Fei Teng, Mao Zeng. 2023-04-18. Comparison of post-Minkowskian and self-force expansions: Scattering in a scalar charge toy model. https://doi.org/10.1103/physrevd.108.024025

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