Binary systems around a black hole (Q701989)

The authors suggest a novel technique that makes the study of small massive objects orbiting around a fixed structure possible, i.e., a mean gravitational field that varies much slower than the local force generated by the orbiting particles. The motion equations are obtained in two different ways. In the first, the Newtonian gravitational potential among the particles is considered as a zeroth order perturbation to a primarily given exact solution of the Einstein field equations. The approximate geodesic equations for the perturbed metric are the equation of motion of the interacting particles. In the second derivation, the authors construct within the Newtonian gravity a quadri-force. Then in the geodesic equations obtained from the fixed source metric, the Newtonian field is treated as an external force acting in each particle, the authors obtain then the same motion equations derived in the first approach. Notice that in this scenario the damping due to the emission of gravitational radiation is not considered. The authors present then a simple application of the above described method. In the context of Schwarzschild geometry, planar interacting orbits are studied, and the results are compared with the equivalent situation in the usual Newtonian theory. When the particles are close enough to the black hole, a great difference in the stability of the studied systems are observed. The most remarkable result is that in the approximate general relativistic approach the generation of binary systems is favored compared with the equivalent pure Newtonian situation. In \(n\)-body simulations the production of binary systems is a key issue in the formation of astrophysical structures as galaxies and star clusters.