Abstract

The binary black holes (BBHs) formed near the supermassive black holes (SMBHs) in the galacticnuclei would undergo eccentricity excitation due to the gravitational perturbations from the SMBH and therefore merger more efficiently. In this paper, we study the coupling of the three body 1st post-Newtonian (pN) effects with the spin effects from the SMBH in the hierarchical triple system.The three body 1pN effects yielding the de-Sitter precession is usually decoupled in the secular dynamics, while it couples to the spin of SMBH through the Lense-Thirring precession of the outer orbital plane. This coupling includes both the precessions of the inner orbit angular momentum and the Runge-Lenz vector around the outer orbit angular momentum in a general reference frame. Our general argument on the coupling of the three body 1pN effects in three body systems could be extended to any other situation as long as the outer orbital plane evolves.

https://arxiv.org/pdf/2004.09390v1.pdf