# Spin-orbit precession along eccentric orbits for extreme mass ratio black hole binaries and its effective-one-body transcription

## TL;DR

This paper analytically calculates spin-orbit precession for eccentric orbits around Schwarzschild black holes using gravitational self-force methods and integrates these results into the Effective-One-Body framework, enhancing the modeling of black hole binaries.

## Contribution

It provides the first analytical self-force calculation of spin-orbit precession for eccentric orbits and incorporates these results into the EOB formalism, revealing new contributions to the spin-orbit couplings.

## Key findings

- Derived the second gyro-gravitomagnetic ratio $g_{S_*}$ up to order $p_r^2/r^4$.
- Transcribed self-force results into the EOB Hamiltonian, improving waveform models.
- Identified new linear-in-mass-ratio contributions to spin-orbit interactions.

## Abstract

In this work we present an analytical gravitational self-force calculation of the spin-orbit precession along an eccentric orbit around a Schwarzschild black hole, following closely the recent prescription of Akcay, Dempsey, and Dolan. We then transcribe this quantity within the Effective-One-Body (EOB) formalism, thereby determining several new, linear-in-mass-ratio, contributions in the post-Newtonian expansion of the spin-orbit couplings entering the EOB Hamiltonian. Namely, we determine the second gyro-gravitomagnetic ratio $g_{S_*}(r,p_r,p_{\phi})$ up to order $p_r^2/r^4$ included.