# Spinning-black-hole scattering and the test-black-hole limit at second post-Minkowskian order

## TL;DR

This paper extends the gravitational scattering mapping of black holes to second post-Minkowskian order, enabling better modeling of spinning binary black hole dynamics by connecting complex two-body interactions to simpler test-body scenarios.

## Contribution

It introduces a 2PM order extension of the black hole scattering mapping, validated against known analytical results and the test-BH limit, aiding in modeling spinning binary black holes.

## Key findings

- Mapping at 2PM order is consistent with post-Newtonian results.
- Mapping aligns with the test-BH limit.
- Potential to improve effective-one-body models.

## Abstract

Recently, the gravitational scattering of two black holes (BHs) treated at the leading order in the weak-field, or post-Minkowskian (PM), approximation to General Relativity has been shown to map bijectively onto a simpler effectively one-body process: the scattering of a test BH in a stationary BH spacetime. Here, for BH spins aligned with the orbital angular momentum, we propose a simple extension of that mapping to 2PM order. We provide evidence for the validity and utility of this 2PM mapping by demonstrating its compatibility with all known analytical results for the conservative local-in-time dynamics of binary BHs in the post-Newtonian (weak-field and slow-motion) approximation and, separately, in the test-BH limit. Our result could be employed in the construction of improved effective-one-body models for the conservative dynamics of inspiraling spinning binary BHs.