Gravitational partial-wave absorption from scattering amplitudes
Rafael Aoude, Alexander Ochirov
Abstract
A bstract We study gravitational absorption effects using effective on-shell scattering amplitudes. We develop an in-in probability-based framework involving plane- and partial-wave coherent states for the incoming wave to describe the interaction of the wave with a black hole or another compact object. We connect this framework to a simplified single-quantum analysis. The basic ingredients are mass-changing three-point amplitudes, which model the leading absorption effects and a spectral-density function of the black hole. As an application, we consider a non-spinning black hole that may start spinning as a consequence of the dynamics. The corresponding amplitudes are found to correspond to covariant spin-weighted spherical harmonics, the properties of which we formulate and make use of. We perform a matching calculation to general-relativity results at the cross-section level and derive the effective absorptive three-point couplings. They are found to behave as $$ \mathcal{O}\left({G}_{\textrm{Newton}}^{s+1}\right) $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>O</mml:mi> <mml:mfenced> <mml:msubsup> <mml:mi>G</mml:mi> <mml:mtext>Newton</mml:mtext> <mml:mrow> <mml:mi>s</mml:mi> <mml:mo>+</mml:mo> <mml:mn>1</mml:mn> </mml:mrow> </mml:msubsup> </mml:mfenced> </mml:math> , where s is the spin of the outgoing massive state.