# New gravitational self-force analytical results for eccentric equatorial orbits around a Kerr black hole: gyroscope precession

## TL;DR

This paper analytically calculates the gravitational self-force correction to gyroscope precession for slightly eccentric equatorial orbits around Kerr black holes, extending previous Schwarzschild results with high-order accuracy.

## Contribution

It provides the first high-order analytical self-force correction results for gyroscope precession in Kerr spacetime, including eccentricity and rotation effects.

## Key findings

- Results accurate to 9.5 post-Newtonian order.
- Second order in eccentricity and rotation parameter.
- Post-Newtonian validation using spinning binary Hamiltonian.

## Abstract

We analytically compute the gravitational self-force correction to the gyroscope precession along slightly eccentric equatorial orbits in the Kerr spacetime, generalizing previous results for the Schwarzschild spacetime. Our results are accurate through the 9.5 post-Newtonian order and to second order in both eccentricity and rotation parameter. We also provide a post-Newtonian check of our results based on the currently known Hamiltonian for spinning binaries.