# Gravitational scattering of two black holes at the fourth post-Newtonian approximation

## TL;DR

This paper calculates the scattering angle of two spinning black holes during hyperbolic encounters using the fourth post-Newtonian approximation and the Effective-One-Body formalism, including tail effects at next-to-next-to-leading order.

## Contribution

It provides a novel computation of the gauge-invariant scattering angle for spinning black holes at high post-Newtonian order, incorporating nonlocal tail effects.

## Key findings

- Computed scattering angle at 4PN order for spinning black holes.
- Included tail effects using a generalized time-localization method.
- Enhanced understanding of unbound black hole encounters.

## Abstract

We compute the (center-of-mass frame) scattering angle $\chi$ of hyperboliclike encounters of two spinning black holes, at the fourth post-Newtonian approximation level for orbital effects, and at the next-to-next-to-leading order for spin-dependent effects. We find it convenient to compute the gauge-invariant scattering angle (expressed as a function of energy, orbital angular momentum and spins) by using the Effective-One-Body formalism. The contribution to scattering associated with nonlocal, tail effects is computed by generalizing to the case of unbound motions the method of time-localization of the action introduced in the case of (small-eccentricity) bound motions by Damour, Jaranowski and Sch\"afer [Phys.\ Rev.\ D {\bf 91}, no. 8, 084024 (2015)].