Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering

Dogan Akpinar, Vittorio del Duca, Riccardo Gonzo

Abstract

Building on recent approaches, we develop an effective field theory for the interaction of spinning particles modeling Kerr black holes within the gravitational self-force expansion. To incorporate dimensional regularization into this framework, we analyze the higher-dimensional metric arising from the minimal coupling solution, comparing it against the Myers-Perry black hole and its particle description. We then derive the 1SF self-force effective action up to quadratic order in the spin expansion, identifying a new type of spinning recoil term that arises from integrating out the heavy dynamics. Next, we study the 1SF metric perturbation both from the traditional self-force perspective and through the diagrammatic background field expansion, making contact with the radiative waveform. This leads us to consider a novel recursion relation for the curved space 1SF Compton amplitude, which we study up to one-loop in the wave regime and compare with the flat space one-loop Compton for Kerr up to quadratic order in spin. Finally, we investigate the 1SF spinning Compton amplitude in the eikonal regime, clarifying how strong-field effect -- such as the location of the separatrix -- emerge from the resummation of the perturbative weak-field expansion.

The spinning self-force EFT: 1SF waveform recursion relation and Compton scattering

Abstract

Building on recent approaches, we develop an effective field theory for the interaction of spinning particles modeling Kerr black holes within the gravitational self-force expansion. To incorporate dimensional regularization into this framework, we analyze the higher-dimensional metric arising from the minimal coupling solution, comparing it against the Myers-Perry black hole and its particle description. We then derive the 1SF self-force effective action up to quadratic order in the spin expansion, identifying a new type of spinning recoil term that arises from integrating out the heavy dynamics. Next, we study the 1SF metric perturbation both from the traditional self-force perspective and through the diagrammatic background field expansion, making contact with the radiative waveform. This leads us to consider a novel recursion relation for the curved space 1SF Compton amplitude, which we study up to one-loop in the wave regime and compare with the flat space one-loop Compton for Kerr up to quadratic order in spin. Finally, we investigate the 1SF spinning Compton amplitude in the eikonal regime, clarifying how strong-field effect -- such as the location of the separatrix -- emerge from the resummation of the perturbative weak-field expansion.

Paper Structure

This paper contains 11 sections, 153 equations, 4 figures.

Table of Contents

  1. Motivation and introduction
  2. Higher-dimensional rotating metrics from spinning point particles
  3. The spinning self-force EFT
  4. 1SF metric perturbation: traditional vs diagrammatic approach
  5. Kerr Compton amplitude: Post-Minkowskian vs self-force
  6. Conclusions and future directions
  7. Simplest rotating metric for a minimally coupled spinning particle
  8. The non-minimal dimension-dependent couplings from the Myers-Perry solution
  9. Details of the GSF expansion of the effective action
  10. Hypergeometric-type functions for the dynamics of a massive particle in Kerr
  11. Box, triangle and bubble coefficients of the one-loop Compton in the wave regime

Figures (4)

  • Figure 1: The 1SF metric diagrammatic expansion.
  • Figure 2: The Kerr background $\left|\psi_{\mathrm{Kerr}}^\sigma\right\rangle$ is described by an off-shell coherent state of virtual gravitons.
  • Figure 3: The stress tensor for Kerr spacetime is given by a sum of perturbative diagrams.
  • Figure 4: The t-channel (left) and s-channel (right) cut configurations contributing to the classical one-loop flat space Compton.