Abstract
We compute classical gravitational observables for the scattering of two spinless black holes in general relativity and mathcal{N} =8 supergravity in the formalism of Kosower, Maybee, and O’Connell (KMOC). We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at mathcal{O} (G3) to all orders in the velocity. These classical observables require the construction and evaluation of certain loop-level quantities which are greatly simplified by harnessing recent advances from scattering amplitudes and collider physics. In particular, we make use of generalized unitarity to construct the relevant loop integrands, employ reverse unitarity, the method of regions, integration-by-parts (IBP), and (canonical) differential equations to simplify and evaluate all loop and phase-space integrals to obtain the classical gravitational observables of interest to two-loop order. The KMOC formalism naturally incorporates radiation effects which enables us to explore these classical quantities beyond the conservative two-body dynamics. From the impulse and the radiated momentum, we extract the scattering angle and the radiated energy. Finally, we discuss universality of the impulse in the high-energy limit and the relation to the eikonal phase.
Highlights
The increasing experimental success of current gravitational wave astronomy [1, 2] combined with the design specifications of future detectors [3,4,5] require theoretical predictions for the classical general relativistic two-body problem to keep up with the experimental accuracy [6].An important tool for the generation of waveform templates, used for detection and parameter estimation, are fast and reliable semi-analytic models of the binary merger
We focus on the gravitational impulse with radiation reaction and the radiated momentum in black hole scattering at O(G3) to all orders in the velocity
We present the results of our computation of the two classical gravitational observables studied in this work: the impulse and the radiated momentum for the scattering of two black holes both in N = 8 supergravity and in general relativity through O(G3)
Summary
The increasing experimental success of current gravitational wave astronomy [1, 2] combined with the design specifications of future detectors [3,4,5] require theoretical predictions for the classical general relativistic two-body problem to keep up with the experimental accuracy [6]. We discuss the scattering kinematics, the relevant classical regions together with a brief reminder of generalized unitarity that allows us to efficiently derive the relevant loop integrands Starting from these integrands, we recall the classical expansion (i.e. the soft expansion in the method of regions [104]) in subsection 3.3, before reducing all integrals to a set of independent masters with the help of integration-by-parts relations. Appendices A, B, C, and D respectively include details on relevant Fourier transformation identities, the relation between the impulse and the scattering angle, unitarity relations and cutting rules to determine certain phase-space integrals from the imaginary part of virtual diagrams, as well as our conventions for the soft master integrals. We are grateful for discussions and comparisons as well as for coordinating publication
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