An analytic framework modeling the gravitational environment of stars orbiting a galactic supermassive black hole

The gravitational interplay between a supermassive black hole and dark matter has set up an exotic environment at the center of a galaxy. In this paper, I present an analytic framework modeling the gravitational influence on the stars orbiting a galactic supermassive black hole. In particular, we discuss two intriguing features, stellar orbital precession and orbital shrinking, which demonstrate an extraordinary gravitational environment near a galactic supermassive black hole. Moreover, I show that these features can be analytically determined by the supermassive black hole mass.