# Orbit classification in a pseudo-Newtonian Copenhagen problem with Schwarzschild-like primaries

## TL;DR

This study explores how relativistic effects and energy levels influence orbital dynamics in a binary black hole system, revealing significant impacts on orbit types and system complexity compared to classical models.

## Contribution

It introduces a pseudo-Newtonian model for the Copenhagen problem with Schwarzschild-like primaries and analyzes the effects of relativistic parameters on orbital behavior.

## Key findings

- Jacobi constant significantly affects orbit final states
- Schwarzschild radius alters orbit character and fractality
- Relativistic effects increase system complexity

## Abstract

We examine the orbital dynamics of the planar pseudo-Newtonian Copenhagen problem, in the case of a binary system of Schwarzschild-like primaries, such as super-massive black holes. In particular, we investigate how the Jacobi constant (which is directly connected with the energy of the orbits) influences several aspects of the orbital dynamics, such as the final state of the orbits. We also determine how the relativistic effects (i.e., the Schwarzschild radius) affect the character of the orbits, by comparing our results with the classical Newtonian problem. Basin diagrams are deployed for presenting all the different basin types, using multiple types of planes with two dimensions. We demonstrate that both the Jacobi constant as well as the Schwarzschild radius highly influence the character of the orbits, as well as the degree of fractality of the dynamical system.