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High Energy Physics - Theory, hep-th,General Relativity and Quantum Cosmology, gr-qc
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.
