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Gravitational Bremsstrahlung from Reverse Unitarity

Enrico Herrmann1, Julio Parra-Martinez2, Michael S. Ruf3, and Mao Zeng4

  • 1Mani L. Bhaumik Institute for Theoretical Physics, UCLA Department of Physics and Astronomy, Los Angeles, California 90095, USA
  • 2Walter Burke Institute for Theoretical Physics, California Institute of Technology, Pasadena, California 91125, USA
  • 3Physikalisches Institut, Albert-Ludwigs Universität Freiburg, D-79104 Freiburg, Germany
  • 4Rudolf Peierls Centre for Theoretical Physics, University of Oxford, Parks Road, Oxford OX1 3PU, United Kingdom

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Phys. Rev. Lett. 126, 201602 – Published 17 May, 2021

DOI: https://doi.org/10.1103/PhysRevLett.126.201602

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(G3), and all orders in velocity. By analytic continuation into the bound state regime, we obtain the O(G3) 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.

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Phys. Rev. Lett. 126, 201602– Published 17 May, 2021
  • Received 4 February 2021
  • Accepted 15 April 2021
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