Classical gravitational scattering amplitude at <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="script">O</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:msup><mml:mi>G</mml:mi><mml:mn>2</mml:mn></mml:msup><mml:msubsup><mml:mi>S</mml:mi><mml:mn>1</mml:mn><mml:mi>∞</mml:mi></mml:msubsup><mml:msubsup><mml:mi>S</mml:mi><mml:mn>2</mml:mn><mml:mi>∞</mml:mi></mml:msubsup><mml:mo stretchy="false">)</mml:mo></mml:math>
Rafael Aoude, Kays Haddad, Andreas Helset
Abstract
We calculate the scattering amplitude of two rotating objects with the linear-in-curvature spin-induced multipoles of Kerr black holes at $\mathcal{O}({G}^{2})$ 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 $\mathcal{O}({G}^{2})$. 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.