Effective one body Hamiltonian of two spinning black-holes with next-to-next-to-leading order spin-orbit coupling

TL;DR

This paper extends the effective-one-body Hamiltonian for two spinning black holes to include next-to-next-to-leading order spin-orbit effects, improving the accuracy of binary black hole dynamics modeling.

Contribution

It provides the first NNLO spin-orbit Hamiltonian within the EOB framework, enhancing the precision of binary black hole simulations.

Findings

NNLO spin-orbit terms moderate the NLO effects in circular orbits.

The Hamiltonian reproduces test-particle limit spin-orbit coupling.

Improves modeling of spinning black-hole binaries.

Abstract

Building on the recently computed next-to-next-to-leading order (NNLO) post-Newtonian (PN) spin-orbit Hamiltonian for spinning binaries \cite{Hartung:2011te} we extend the effective-one-body (EOB) description of the dynamics of two spinning black-holes to NNLO in the spin-orbit interaction. The calculation that is presented extends to NNLO the next-to-leading order (NLO) spin-orbit Hamiltonian computed in Ref. \cite{Damour:2008qf}. The present EOB Hamiltonian reproduces the spin-orbit coupling through NNLO in the test-particle limit case. In addition, in the case of spins parallel or antiparallel to the orbital angular momentum, when circular orbits exist, we find that the inclusion of NNLO spin-orbit terms moderates the effect of the NLO spin-orbit coupling.