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arXiv · 2508.00087

Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime

Samuel D. Upton·Barry Wardell·Adam Pound·Niels Warburton·Leor Barack
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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.

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Samuel D. Upton, Barry Wardell, Adam Pound, Niels Warburton, Leor Barack. 2025-07-31. Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime. https://doi.org/10.1103/f9j2-k64r

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