Not yet reviewed by Pith; the record is open.

Although gravitational waves tend to erase eccentricity of an inspiraling binary system, ellipticity can be generated in the presence of surrounding matter. We present a semi-analytical method for understanding the eccentricity distribution of binary black holes in the presence of a supermassive black hole in a galactic center. Given a matter distribution, we show how to determine the resultant eccentricity analytically in the presence of both tidal forces and evaporation up to one cutoff and one matter-distribution-independent function, paving the way for understanding the environment of detected inspiraling black holes. We furthermore generalize Kozai-Lidov dynamics to situations where perturbation theory breaks down for short time intervals, allowing more general angular momentum exchange, such that eccentricity is generated even when all bodies orbit in the same plane.