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

Miller, Jeremy, Wardell, Barry and Pound, Adam (2016) Second-order perturbation theory: the problem of infinite mode coupling. Physical Review D, 94 (104018), 1-18. (doi:10.1103/PhysRevD.94.104018).

Record type: Article

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.

Text

toy_model_submission_version.pdf - Accepted Manuscript

Available under License University of Southampton Accepted Manuscript Licence.

Download (153kB)