Abstract
We compute the total radiated momentum carried by gravitational waves during the scattering of two spinless black holes at the lowest order in Newton's constant, O(G^{3}), and all orders in velocity. By analytic continuation into the bound state regime, we obtain the O(G^{3}) energy loss in elliptic orbits. This provides an essential step toward the complete understanding of the third-post-Minkowskian binary dynamics. We employ the formalism of Kosower, Maybee, and O'Connell (KMOC), which relates classical observables to quantum scattering amplitudes, and derive the relevant integrands using generalized unitarity. The subsequent phase-space integrations are performed via the reverse unitarity method familiar from collider physics, using differential equations to obtain the exact velocity dependence from near-static boundary conditions.
Highlights
Introduction.—There has been enormous progress in applying scattering amplitude tools such as generalized unitarity [1,2,3] and the double copy [4,5,6,7,8,9], together with effective field theory ideas [10,11,12], to the classical relativistic two-body problem, geared toward applications for current and future gravitational wave detectors [13,14]
We employ the formalism of Kosower, Maybee, and O’Connell (KMOC), which relates classical observables to quantum scattering amplitudes, and derive the relevant integrands using generalized unitarity
The subsequent phase-space integrations are performed via the reverse unitarity method familiar from collider physics, using differential equations to obtain the exact velocity dependence from near-static boundary conditions
Summary
We compute the total radiated momentum carried by gravitational waves during the scattering of two spinless black holes at the lowest order in Newton’s constant, OðG3Þ, and all orders in velocity. Introduction.—There has been enormous progress in applying scattering amplitude tools such as generalized unitarity [1,2,3] and the double copy [4,5,6,7,8,9], together with effective field theory ideas [10,11,12], to the classical relativistic two-body problem, geared toward applications for current and future gravitational wave detectors [13,14] Such techniques have produced new results for the dynamics of spinless [12,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30] and spinning [31,32,33,34,35,36,37,38,39,40,41,42,43,44] black holes, including finite-size effects [45,46,47,48,49,50,51,52,53]. The basic idea of this approach is to set up a gedanken experiment for the scattering of two wave packets, widely separated by an impact parameter bμ, and measure the change in an observable O, with corresponding quantum operator O, between in and out states
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