Confirm minimal-coupling Compton amplitude matches Kerr black hole dynamics via BHPT

Establish, by explicit matching to black hole perturbation theory, that the classical one-loop gravitational Compton amplitude constructed with minimal couplings indeed describes graviton scattering off a Kerr black hole. The confirmation should address the second post-Minkowskian order and include spin contributions up to the quartic order, as computed in this work.

Background

The paper constructs the classical one-loop gravitational Compton amplitude using minimal couplings, which are expected to model the scattering of gravitons off a Kerr black hole. While the amplitude satisfies non-trivial consistency checks such as Weinberg’s infrared factorization and gauge invariance, the authors emphasize that a definitive identification with Kerr requires matching against black hole perturbation theory (BHPT).

Confirming this correspondence is important for validating the amplitude-based approach to Kerr dynamics beyond leading orders and ensuring the reliability of the computed post-Minkowskian contributions, especially with spin effects up to quartic order.