Absorptive effects in black hole scattering
Yilber Fabian Bautista, Yu-tin Huang, Jung-Wook Kim
Abstract
In this paper, we define absorptive Compton amplitudes, which capture the absorption factor for waves of spin-weight- <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>s</a:mi> </a:math> scattering in black hole perturbation theory. At the leading order, in the <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"> <c:mi>G</c:mi> <c:mi>M</c:mi> <c:mi>ω</c:mi> </c:math> expansion, such amplitudes are purely imaginary and expressible as contact terms. Equipped with these amplitudes we compute the mass change in black hole scattering events via the Kosower-Maybee-O’Connell formalism, where the rest mass of a Schwarzschild/Kerr black hole is modified due to absorption of gravitational, electromagnetic, or scalar fields sourced by other compact object. We reproduced the power loss previously computed in the post-Newtonian expansion. The results presented here hold for similar mass ratios and generic spin orientation, while keeping the Kerr spin parameter to lie in the physical region <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"> <e:mi>χ</e:mi> <e:mo>≤</e:mo> <e:mn>1</e:mn> </e:math> .