# Analytical determination of the periastron advance in spinning binaries from self-force computations

## TL;DR

This paper provides the first analytical calculation of the conservative gravitational self-force correction to the periastron advance in spinning black hole binaries, accurate to second order in spin and 9.5 post-Newtonian order.

## Contribution

It introduces a novel analytical method to compute self-force corrections for spinning black holes, extending previous work to include spin effects and higher post-Newtonian accuracy.

## Key findings

- First analytical self-force correction to periastron advance in Kerr spacetime.
- Correction accurate to second order in spin and 9.5 post-Newtonian level.
- New results on gyroscope precession invariant in Kerr spacetime.

## Abstract

We present the first analytical computation of the (conservative) gravitational self-force correction to the periastron advance around a spinning black hole. Our result is accurate to the second order in the rotational parameter and through the 9.5 post-Newtonian level. It has been obtained as the circular limit of the correction to the gyroscope precession invariant along slightly eccentric equatorial orbits in the Kerr spacetime. The latter result is also new and we anticipate here the first few terms only of the corresponding post-Newtonian expansion.