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Classical Gravitational Spinning-Spinless Scattering at O(G^{2}S^{∞}).

Rafael Aoude1, Kays Haddad2,3, Andreas Helset4

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We calculated classical gravitational scattering for spinning and spinless objects using a novel Compton amplitude. This reveals spin structure consistent with Kerr black holes and simplifies complex spin dependencies.

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Area of Science:

  • Theoretical physics
  • Gravitational physics
  • Quantum field theory

Background:

  • The study of gravitational scattering is crucial for understanding extreme astrophysical objects like black holes.
  • Previous calculations were limited in their treatment of spin effects.
  • A new all-spin, opposite-helicity Compton amplitude has recently been developed.

Purpose of the Study:

  • To calculate the classical gravitational scattering amplitude for one spinning and one spinless object at O(G^2) and all orders in spin.
  • To incorporate spin structure conjectured for Kerr black holes into the scattering amplitude.
  • To determine the eikonal phase for aligned-angular-momentum scattering.

Main Methods:

  • Utilizing the recently derived all-spin, opposite-helicity Compton amplitude.
  • Applying considerations of the ultrarelativistic limit to fix remaining parameters.
  • Resumming spin dependence into hypergeometric functions.

Main Results:

  • The classical gravitational scattering amplitude for one spinning and one spinless object was calculated.
  • The derived amplitude exhibits the spin structure conjectured for Kerr black holes.
  • Spin dependence was resummed into hypergeometric functions, and the eikonal phase for aligned-angular-momentum scattering was derived.

Conclusions:

  • The study provides a new method for calculating gravitational scattering amplitudes with spin.
  • The results offer insights into the nature of spinning black holes and their gravitational interactions.
  • The findings pave the way for further investigations into multi-body gravitational dynamics.