  The leading order effect of the spin of a distant supermassive black hole
(SMBH) on the orbit of compact binary revolving around it appears at the 1.5
post Newtonian (PN) expansion through coupling with the inner and outer orbital
angular momenta, and makes an oscillating characteristic contribution to the
secular evolution of the compact binary eccentricity over a long time scale
compared to the Kozai-Lidov dynamics caused by a non-spinning SMBH.
