Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime
Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime
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.
Upton, Samuel D.
f0ff8ac2-2ef0-4a99-b2d6-e55772f34dcf
Wardell, Barry
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Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Warburton, Niels
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Barack, Leor
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4 March 2026
Upton, Samuel D.
f0ff8ac2-2ef0-4a99-b2d6-e55772f34dcf
Wardell, Barry
e57ef389-d765-45e5-aeb8-2a62896da6d9
Pound, Adam
5aac971a-0e07-4383-aff0-a21d43103a70
Warburton, Niels
d441704c-2bd5-4530-9ccc-b610b83e2eb1
Barack, Leor
f08e66d4-c2f7-4f2f-91b8-f2c4230d0298
Upton, Samuel D., Wardell, Barry, Pound, Adam, Warburton, Niels and Barack, Leor
(2026)
Effective source for second-order self-force calculations: quasicircular orbits in Schwarzschild spacetime.
Physical Review D, 113 (6), [064013].
(doi:10.1103/f9j2-k64r).
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.
Text
SecondOrderSource
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Accepted/In Press date: 28 January 2026
Published date: 4 March 2026
Identifiers
Local EPrints ID: 509701
URI: http://eprints.soton.ac.uk/id/eprint/509701
ISSN: 2470-0010
PURE UUID: c9c1fb61-8ae5-4fc3-bace-3a996548ac7b
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Date deposited: 03 Mar 2026 17:36
Last modified: 06 Mar 2026 03:29
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Author:
Samuel D. Upton
Author:
Barry Wardell
Author:
Niels Warburton
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