We describe an on-shell, amplitudes-based approach to incorporating radiation absorption effects in the post-Minkowskian scattering of generic, compact, spinning bodies. Classical spinning observables are recovered by extrapolating to large spin, results calculated with finite quantum spin-s particles using the properties of spin universality and Casimir interpolation. At leading-order our results give a completely general and non-redundant parametrization of absorptive observables in terms of a finite number of Wilson coefficients associated with 3-particle mass and spin-magnitude changing on-shell amplitudes. We denote these semi-fictitious microscopic processes: classical spin transitions. Explicit results for the leading-order impulse due to the absorption of scalar, electromagnetic and gravitational radiation, for spin transitions ∆s = 0, ±1, ±2 are given in a fully interpolated form up to <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msup> <mi>S</mi> <mn>2</mn> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{O}\left({S}^2\right) $</EquationSource> </InlineEquation>, and Casimir independent contributions given up to <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msup> <mi>S</mi> <mn>4</mn> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">$ \mathcal{O}\left({S}^4\right) $</EquationSource> </InlineEquation>. Our explicit results reveal some surprising universal patterns. We find that, up to identification of Wilson coefficients, the Casimir independent contributions to the impulse for spinning-up and spinning-down by the same magnitude |∆s| are identical. For processes where the quantum ∆s < 0 transition is forbidden, the corresponding classical observable is suppressed in powers of S by a predictable amount. Additionally we find that, while for generic non-aligned spin configurations there is a non-zero scattering angle at leading-order, for aligned spin, similar to non-spinning absorption, the scattering angle vanishes and the impulse is purely longitudinal. The formalism and results presented provide a significant extension of the amplitudes-based calculational pipeline for gravitational waveforms from binary black hole and neutron star systems beyond the point-particle approximation.

Classical spin transitions and absorptive scattering

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2026年4月23日

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Juan Pablo Gatica,
Callum R. T. Jones

摘要

We describe an on-shell, amplitudes-based approach to incorporating radiation absorption effects in the post-Minkowskian scattering of generic, compact, spinning bodies. Classical spinning observables are recovered by extrapolating to large spin, results calculated with finite quantum spin-s particles using the properties of spin universality and Casimir interpolation. At leading-order our results give a completely general and non-redundant parametrization of absorptive observables in terms of a finite number of Wilson coefficients associated with 3-particle mass and spin-magnitude changing on-shell amplitudes. We denote these semi-fictitious microscopic processes: classical spin transitions. Explicit results for the leading-order impulse due to the absorption of scalar, electromagnetic and gravitational radiation, for spin transitions ∆s = 0, ±1, ±2 are given in a fully interpolated form up to $O (S^{2})$ $ \mathcal{O}\left({S}^2\right) $ , and Casimir independent contributions given up to $O (S^{4})$ $ \mathcal{O}\left({S}^4\right) $ . Our explicit results reveal some surprising universal patterns. We find that, up to identification of Wilson coefficients, the Casimir independent contributions to the impulse for spinning-up and spinning-down by the same magnitude |∆s| are identical. For processes where the quantum ∆s < 0 transition is forbidden, the corresponding classical observable is suppressed in powers of S by a predictable amount. Additionally we find that, while for generic non-aligned spin configurations there is a non-zero scattering angle at leading-order, for aligned spin, similar to non-spinning absorption, the scattering angle vanishes and the impulse is purely longitudinal. The formalism and results presented provide a significant extension of the amplitudes-based calculational pipeline for gravitational waveforms from binary black hole and neutron star systems beyond the point-particle approximation.