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<p>Quantum higher-spin theory applied to Compton amplitudes has proven to be surprisingly useful for elucidating Kerr black hole dynamics. Here we apply the framework to compute scattering amplitudes and observables for a binary system of two rotating black holes, at second post-Minkowskian order, and to all orders in the spin-multipole expansion for certain quantities. Starting from the established three-point and conjectured Compton quantum amplitudes, the infinite-spin limit gives classical amplitudes that serve as building blocks that we feed into the unitarity method to construct the 2-to-2 one-loop amplitude. We give scalar box, vector box, and scalar triangle coefficients to all orders in spin, where the latter are expressed in terms of Bessel-like functions. Using the Kosower-Maybee-O’Connell formalism, the classical 2PM impulse is computed, and in parallel we work out the scattering angle and eikonal phase. We give novel all-order-in-spin formulae for certain contributions, and the remaining ones are given up to <InlineEquation ID="IEq1"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msup> <mi>S</mi> <mn>11</mn> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({S}^{11}\right) \)</EquationSource> </InlineEquation>. Since Kerr 2PM dynamics beyond <InlineEquation ID="IEq2"> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">O</mi> <mfenced close=")" open="("> <msup> <mi>S</mi> <mrow> <mo>≥</mo> <mn>5</mn> </mrow> </msup> </mfenced> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{O}\left({S}^{\ge 5}\right) \)</EquationSource> </InlineEquation> is as of yet not completely settled, this work serves as a useful reference for future studies.</p>

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Binary Kerr black-hole scattering at 2PM from quantum higher-spin Compton

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  • 发表日期：

    2025年7月28日

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  • Lara Bohnenblust,
  • Lucile Cangemi,
  • Henrik Johansson,
  • Paolo Pichini

摘要

Quantum higher-spin theory applied to Compton amplitudes has proven to be surprisingly useful for elucidating Kerr black hole dynamics. Here we apply the framework to compute scattering amplitudes and observables for a binary system of two rotating black holes, at second post-Minkowskian order, and to all orders in the spin-multipole expansion for certain quantities. Starting from the established three-point and conjectured Compton quantum amplitudes, the infinite-spin limit gives classical amplitudes that serve as building blocks that we feed into the unitarity method to construct the 2-to-2 one-loop amplitude. We give scalar box, vector box, and scalar triangle coefficients to all orders in spin, where the latter are expressed in terms of Bessel-like functions. Using the Kosower-Maybee-O’Connell formalism, the classical 2PM impulse is computed, and in parallel we work out the scattering angle and eikonal phase. We give novel all-order-in-spin formulae for certain contributions, and the remaining ones are given up to O S 11 \( \mathcal{O}\left({S}^{11}\right) \) . Since Kerr 2PM dynamics beyond O S ≥ 5 \( \mathcal{O}\left({S}^{\ge 5}\right) \) is as of yet not completely settled, this work serves as a useful reference for future studies.