How does a black hole capture an approaching star and force it to start an elliptical orbit? Let's assume that a standing still black hole attractor can have a star orbiting it in an orbit if the star was somehow a result of the same past proccesses as the black hole.So the star must be on a given point with right velocity and direction to be in an elliptical orbit around the BH.If the star was approaching from a distant location it will take the parabolic or hyperbolic trayectory.Is the trick to capture a free star by a BH to move slightly towards or away from the approaching star?
 A: If a black hole* is approached by a star which was originally unbound from the black hole's gravity, the star will follow a hyperbolic object: it will have some form of close approach, and then move away in a quasi-straight line with nonzero kinetic energy at infinity.
For the star to get captured into a bound orbit, there needs to be an interaction with some third object, which can dissipate some of the energy from the orbit. This is typically another star in the neighbourhood, which has a close-ish encounter with our prospective capture when the latter is close to the black hole. This third body might:

*

*already be captured, and be lifted to a higher, more energetic orbit

*already be captured, and be set free by the encounter

*also be in a hyperbolic, unbound orbit, and end up with even more energy going out

The details will depend on the precise initial conditions.


*${}$ Note that nothing here is specific to a black hole. If the incoming star remains well away from the event horizon (and it is extremely hard for a random incoming orbit to get that close, as it will generically have too much energy and angular momentum), the entire interaction can be described with Newtonian gravity in the point-mass approximation. As such, you get the same dynamics with e.g. planetesimals coalescing around a massive star, the formation of binary systems inside a globular cluster, etc.

