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The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order

N. Emil J. Bjerrum-Bohr, Gang Chen, Carl Jordan Eriksen, Nabha Shah

Abstract

We utilize various computational techniques in flat and curved backgrounds to calculate the classical gravitational Compton amplitude up to the second post-Minkowskian order. Our novel result supports the use of worldline quantum field theory in non-trivial background spacetimes to obtain new theoretical insights that can both enhance computational efficiency and provide useful cross-checks of results, particularly in the context of classical binary black hole mergers.

The gravitational Compton amplitude from flat and curved spacetimes at second post-Minkowskian order

Abstract

We utilize various computational techniques in flat and curved backgrounds to calculate the classical gravitational Compton amplitude up to the second post-Minkowskian order. Our novel result supports the use of worldline quantum field theory in non-trivial background spacetimes to obtain new theoretical insights that can both enhance computational efficiency and provide useful cross-checks of results, particularly in the context of classical binary black hole mergers.

Paper Structure

This paper contains 14 sections, 119 equations, 1 figure, 1 table.

Table of Contents

  1. Introduction
  2. Worldline quantum field theory in flat and curved space
  3. Weak-field expansion
  4. Curved space expansion
  5. The classical Compton amplitude
  6. First post-Minkowskian order Compton amplitude
  7. Second post-Minkowskian order Compton amplitude
  8. Diagrammatic expansion
  9. Result
  10. Conclusion
  11. Fourier transform
  12. Master integrals
  13. Scaleless contributions to the worldline action
  14. Second post-Minkowskian order Compton amplitude from heavy-mass effective field theory

Figures (1)

  • Figure 1: The cut bubble $\mathcal{K}_1$, the cut triangle $\mathcal{K}_2$, and the cut box $\mathcal{K}_3$. The red line signifies the propagator that is cut.