Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime
Abstract
Recent years have seen the first production of "post-adiabatic" gravitational-waveform models based on second-order gravitational self-force theory. These models rely on calculations of an effective source in the perturbative second-order Einstein equation. Here, for the first time, we detail the calculation of the effective source in a Schwarzschild background, which underlies the second-order self-force results in [Phys. Rev. Lett. 127, 151102 (2021); ibid. 128, 231101 (2022); ibid. 130, 241402 (2023)]. The source is designed for use in the multiscale form of the Lorenz-gauge Einstein equation, decomposed in tensor spherical harmonics, or in the analogous second-order Teukolsky equation. It involves, among other things, contributions from (i) quadratic coupling of first-order field modes, (ii) the slow evolution of first-order fields, (iii) quadratic products of a first-order puncture field, and (iv) the second-order puncture field. We validate each of these pieces through numerical and analytical tests.
Keywords
Cite
@article{arxiv.2508.00087,
title = {Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime},
author = {Samuel D. Upton and Barry Wardell and Adam Pound and Niels Warburton and Leor Barack},
journal= {arXiv preprint arXiv:2508.00087},
year = {2026}
}
Comments
38 pages, 15 figures, 2 tables. Version to appear in PRD