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

TL;DR

This study explores the orbital dynamics of a test particle in a pseudo-Newtonian binary black hole system, classifying orbit types and analyzing how system parameters influence orbital behavior and stability.

Contribution

It introduces a detailed classification of orbits in a pseudo-Newtonian binary black hole system using SALI chaos indicator and explores the transition from Newtonian to pseudo-Newtonian regimes.

Findings

Orbit types depend strongly on the Jacobi constant and Schwarzschild radius.

Transition from Newtonian to pseudo-Newtonian dynamics affects orbital structures.

Distribution of escape and collision times varies with system parameters.

Abstract

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