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arXiv · 2305.09724

Frequency-domain approach to self-force in hyperbolic scattering

Christopher Whittall·Leor Barack
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Abstract

We develop a frequency-domain method for calculating the self-force acting on a scalar charge on a fixed scattering geodesic in Schwarzschild spacetime. Existing frequency-domain methods, which are tailored for bound orbits, are inadequate here for several reasons. One must account for the continuous spectrum in the scattering problem, deal with slowly-convergent radial integrals that are hard to evaluate numerically, and confront the inapplicability of the standard self-force method of "extended homogeneous solutions", which only works for compactly supported sources. We tackle each of these issues in turn, and then present a full numerical implementation, in which we calculate the self-force correction to the scatter angle due to scalar-field back-reaction. We perform a range of internal validation tests, as well as ones based on comparison with existing time-domain results. We discuss the merits and remaining limitations of our method, and outline directions for future work.

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BibTeXRIS

Christopher Whittall, Leor Barack. 2023-05-16. Frequency-domain approach to self-force in hyperbolic scattering. https://doi.org/10.1103/physrevd.108.064017

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