Effective-one-body Hamiltonian with next-to-leading order spin-spin coupling

TL;DR

This paper develops an improved effective-one-body Hamiltonian incorporating next-to-leading order spin-spin couplings for binary systems with arbitrary spins, extending previous work limited to equatorial orbits.

Contribution

It introduces a systematic method to include NLO spin-spin effects into the EOB Hamiltonian for general orbits, reducing complexity from 25 to 12 parameters.

Findings

Extended EOB Hamiltonian to general spin orientations.

Reduced the number of parameters needed to describe NLO spin-spin effects.

Ensured consistency with the test-mass limit.

Abstract

We propose a way of including the next-to-leading (NLO) order spin-spin coupling into an effective-one-body (EOB) Hamiltonian. This work extends [S. Balmelli and P. Jetzer, Phys. Rev. D 87, 124036 (2013)], which is restricted to the case of equatorial orbits and aligned spins, to general orbits with arbitrary spin orientations. This is done applying appropriate canonical phase-space transformations to the NLO spin-spin Hamiltonian in Arnowitt-Deser-Misner (ADM) coordinates, and systematically adding "effectiv" quantities at NLO to all spin-squared terms appearing in the EOB Hamiltonian. As required by consistency, the introduced quantities reduce to zero in the test- mass limit. We expose the result both in a general gauge and in a gauge-fixed form. The last is chosen such as to minimize the number of new coefficients that have to be inserted into the effective spin squared. As a result, the 25 parameters that describe the ADM NLO spin-spin dynamics get condensed into only 12 EOB terms.