Binary Kerr black-hole scattering at 2PM from quantum higher-spin Compton
Lara Bohnenblust, Lucile Cangemi, Henrik Johansson, Paolo Pichini
Abstract
A bstract 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 $$ \mathcal{O}\left({S}^{11}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mi>S</mml:mi> <mml:mn>11</mml:mn> </mml:msup> </mml:mfenced> </mml:math> . Since Kerr 2PM dynamics beyond $$ \mathcal{O}\left({S}^{\ge 5}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msup> <mml:mi>S</mml:mi> <mml:mrow> <mml:mo>≥</mml:mo> <mml:mn>5</mml:mn> </mml:mrow> </mml:msup> </mml:mfenced> </mml:math> is as of yet not completely settled, this work serves as a useful reference for future studies.