Binary Systems Around a Black Hole

We present a novel method to study interacting orbits in a fixed mean gravitational field associated with a solution of the Einstein field equations. The idea is to consider the Newton gravity among the orbiting particles in a geometry given by the main source. For this purpose, the motion equations are obtained in two different but equivalent ways. The particles can either be considered as a zeroth order (static) perturbation to the given metric or as an external Newtonian force in the geodesic equations. After obtaining the motion equations we perform simulations of two and three interacting particles moving around a black hole, i.e., in a Schwarzschild geometry. We also compare with the equivalent Newtonian problem and note differences in the stability, e.g., binary systems are found only in the general relativistic approach.