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Resumming Spinning Black Hole Dynamics at Third Post-Minkowskian Order

N. Emil J. Bjerrum-Bohr, Gang Chen, Konstantinos Papadimos, Yuexiang Zhang

Abstract

We investigate the relativistic scattering of spinning black holes using modern amplitude methods within a heavy-mass effective field theory formalism at third post-Minkowskian order. Using a systematic self-force expansion up to first order in the mass ratio, the gravitational amplitude and the associated eikonal-like phase are computed for a spin-aligned binary system comprising a heavy and a light black hole up to fifth order in the total spin and up to quadratic order in the spin of the light black hole. We also consider the resummation of the heavy black hole's spin in both the probe limit and the radiation-reaction sector, and verify that the resulting phase displays the characteristic ring singularity features associated with the Kerr metric.

Resumming Spinning Black Hole Dynamics at Third Post-Minkowskian Order

Abstract

We investigate the relativistic scattering of spinning black holes using modern amplitude methods within a heavy-mass effective field theory formalism at third post-Minkowskian order. Using a systematic self-force expansion up to first order in the mass ratio, the gravitational amplitude and the associated eikonal-like phase are computed for a spin-aligned binary system comprising a heavy and a light black hole up to fifth order in the total spin and up to quadratic order in the spin of the light black hole. We also consider the resummation of the heavy black hole's spin in both the probe limit and the radiation-reaction sector, and verify that the resulting phase displays the characteristic ring singularity features associated with the Kerr metric.
Paper Structure (15 sections, 98 equations)

This paper contains 15 sections, 98 equations.

Table of Contents

  1. Introduction
  2. Convenient choices of kinematics and conventions
  3. Tree amplitudes
  4. The spinning three-point amplitude
  5. Compton amplitude
  6. Five-point amplitude up to quadratic order
  7. Binary scattering at zero self-force order
  8. Binary scattering at first self-force order
  9. Spin resummation and the Kerr singularity at third post-Minkowskian order
  10. Conclusions & Outlook
  11. Tensor Decomposition
  12. The General Method
  13. Example: Decomposition of the Levi-Civita Tensor
  14. Amplitudes at first self-force order
  15. The eikonal-like phase at first self-force order