At the center of a distant galaxy, a supermassive black hole is surrounded by a flat, rotating disk of gas and dust — a giant cosmic funnel of matter. A small compact object, such as another stellar-mass black hole, may find itself in this disk. It moves along its orbit, but every so often it pierces the disk from top to bottom, like a needle stitching through fabric. Each crossing is an encounter with gas resistance that gradually alters its path.

A team of researchers built a mathematical model to trace the long-term evolution of such a system. They used the exact equations of motion in curved spacetime (Kerr geodesics) and described the disk's influence through two effects: the object's capture of matter and dynamical friction — deceleration due to gravitational interaction with the gas. The process unfolds in two stages. First, the orbit quickly rotates until it lies in the disk plane, like a spinning top that stops wobbling and stands upright. Then, much more slowly, its elongation fades: it transforms from an ellipse into an almost perfect circle.

The scientists also tested how the choice of gas disk model affects the result. The Novikov-Thorne model assumes a denser, thinner disk, while the Sirko-Goodman model assumes a puffier, more rarefied one. In the latter case, the braking is weaker, and the orbital evolution slows down. The black hole's own rotation, its spin, however, has almost no effect on how quickly the object loses its orbital elongation. These results are important for understanding what happens in the cores of active galaxies and may shed light on the nature of the repeating X-ray flares sometimes observed there.