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

TL;DR

This paper extends the Effective One Body (EOB) approach to model the dynamics of two spinning black holes by incorporating next-to-leading order spin-orbit coupling, improving the accuracy of gravitational wave predictions.

Contribution

The authors develop a NLO spin-orbit Hamiltonian within the EOB framework, including a generalized Hamilton-Jacobi equation and a Kerr-type metric with resummed coefficients, advancing binary black hole modeling.

Findings

NLO spin-orbit terms significantly affect the last stable orbit characteristics.

The new Hamiltonian accurately computes binding energy and orbital frequency for spinning black holes.

Inclusion of NLO terms moderates the dynamics for large parallel spins.

Abstract

Using a recent, novel Hamiltonian formulation of the gravitational interaction of spinning binaries, we extend the Effective One Body (EOB) description of the dynamics of two spinning black holes to next-to-leading order (NLO) in the spin-orbit interaction. The spin-dependent EOB Hamiltonian is constructed from four main ingredients: (i) a transformation between the ``effective'' Hamiltonian and the ``real'' one, (ii) a generalized effective Hamilton-Jacobi equation involving higher powers of the momenta, (iii) a Kerr-type effective metric (with Pad\'e-resummed coefficients) which depends on the choice of some basic ``effective spin vector'' $\bf{S}_{\rm eff}$, and which is deformed by comparable-mass effects, and (iv) an additional effective spin-orbit interaction term involving another spin vector $\bsigma$. As a first application of the new, NLO spin-dependent EOB Hamiltonian, we compute the binding energy of circular orbits (for parallel spins) as a function of the orbital frequency, and of the spin parameters. We also study the characteristics of the last stable circular orbit: binding energy, orbital frequency, and the corresponding dimensionless spin parameter $\hat{a}_{\rm LSO}\equiv c J_{\rm LSO}/\boldsymbol(G(H_{\rm LSO}/c^2)^2\boldsymbol)$. We find that the inclusion of NLO spin-orbit terms has a significant ``moderating'' effect on the dynamical characteristics of the circular orbits for large and parallel spins.