Accelerated Schwarzschild orbits in an external tidal field

Abstract

We study the orbit of a point particle in a hierarchical three-body system composed of an extreme mass ratio inner binary, and a distant perturber. The inner binary consists of a Schwarzschild black hole at the center with a test particle orbiting around it. The orbital evolution equations were obtained using the method of osculating orbits, treating the problem as motion along a Schwarzschild geodesic which is then accelerated due to the tidal field of the perturber. We also track the precession of the periastron over long time scales.