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The dynamics of a test particle in a non-spinning binary black hole system ofequal masses is numerically investigated. The binary system is modeled in thecontext of the pseudo-Newtonian circular restricted three-body problem, suchthat the primaries are separated by a fixed distance and move in a circularorbit around each other. In particular, the Paczy\'{n}ski-Wiita potential isused for describing the gravitational field of the two non-Newtonian primaries.The orbital properties of the test particle are determined through theclassification of the initial conditions of the orbits, using several values ofthe Jacobi constant, in the Hill's regions of possible motion. The initialconditions are classified into three main categories: (i) bounded, (ii)escaping and (iii) displaying close encounters. Using the smaller alignmentindex (SALI) chaos indicator, we further classify bounded orbits into regular,sticky or chaotic. To gain a complete view of the dynamics of the system, wedefine grids of initial conditions on different types of two-dimensionalplanes. The orbital structure of the configuration plane, along with thecorresponding distributions of the escape and collision/close encounter times,allow us to observe the transition from the classical Newtonian to thepseudo-Newtonian regime. Our numerical results reveal a strong dependence ofthe properties of the considered basins with the Jacobi constant as well aswith the Schwarzschild radius of the black holes.

Orbit classification in an equal-mass non-spinning binary black hole pseudo-Newtonian system