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arXiv · 1608.06783

Second-order perturbation theory: the problem of infinite mode coupling

Jeremy Miller·Barry Wardell·Adam Pound
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Abstract

Second-order self-force computations, which will be essential in modeling extreme-mass-ratio inspirals, involve two major new difficulties that were not present at first order. One is the problem of large scales, discussed in [Phys. Rev. D 92, 104047 (2015)]. Here we discuss the second difficulty, which occurs instead on small scales: if we expand the field equations in spherical harmonics, then because the first-order field contains a singularity, we require an arbitrarily large number of first-order modes to accurately compute even a single second-order mode. This is a generic feature of nonlinear field equations containing singularities, allowing us to study it in the simple context of a scalar toy model in flat space. Using that model, we illustrate the problem and demonstrate a robust strategy for overcoming it.

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Jeremy Miller, Barry Wardell, Adam Pound. 2016-08-24. Second-order perturbation theory: the problem of infinite mode coupling. https://doi.org/10.1103/physrevd.94.104018

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