Classical gravitational scattering amplitude at <math display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>2</mn></msup><msubsup><mi>S</mi><mn>1</mn><mi>∞</mi></msubsup><msubsup><mi>S</mi><mn>2</mn><mi>∞</mi></msubsup><mo stretchy="false">)</mo></math>

Tourinho Jadallah Aoude, Rafael;et.al.
(2023) Physical review D — Vol. 108 (2023)

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Abstract
We calculate the scattering amplitude of two rotating objects with the linear-in-curvature spin-induced multipoles of Kerr black holes at <math display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math> and all orders in the spins of both objects. This is done including the complete set of contact terms potentially relevant to Kerr-black-hole scattering at <math display="inline"><mi mathvariant="script">O</mi><mo stretchy="false">(</mo><msup><mi>G</mi><mn>2</mn></msup><mo stretchy="false">)</mo></math>. As such, Kerr black holes should be described by this scattering amplitude for a specific choice of values for the contact-term coefficients. The inclusion of all potential contact terms means this amplitude allows for a comprehensive search for structures emerging for certain values of the coefficients, and hence special properties that might be exhibited by Kerr-black-hole scattering. Our result can also act as a template for comparison for future computations of classical gravitational high-spin scattering.
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Tourinho Jadallah Aoude, R., & et al. (2023). Classical gravitational scattering amplitude at <math display=“inline”><mi mathvariant=“script”>O</mi><mo stretchy=“false”>(</mo><msup><mi>G</mi><mn>2</mn></msup><msubsup><mi>S</mi><mn>1</mn><mi>∞</mi></msubsup><msubsup><mi>S</mi><mn>2</mn><mi>∞</mi></msubsup><mo stretchy=“false”>)</mo></math>. Physical review D, 108. https://doi.org/10.1103/PhysRevD.108.024050 (Original work published 2023)