Classification of the trajectories of uncharged particles in the Schwarzschild-Melvin metric

TL;DR

This paper classifies the possible trajectories of uncharged particles in Schwarzschild-Melvin spacetime by analyzing a reduced Hamiltonian system and studying bifurcations of periodic solutions.

Contribution

It provides a detailed classification of particle trajectories and analyzes bifurcations in the reduced Hamiltonian system in Schwarzschild-Melvin spacetime.

Findings

Classification of regions of possible particle motion

Analysis of bifurcations of periodic solutions

Identification of motion types based on energy and momentum

Abstract

This paper investigates the trajectories of neutral particles in the Schwarzschild-Melvin spacetime. After reduction by cyclic coordinates this problem reduces to investigating a two-degree-of-freedom Hamiltonian system that has no additional integral. A classification of regions of possible motion of a particle is performed according to the values of the momentum and energy integrals. Bifurcations of periodic solutions of the reduced system are analyzed using a Poincare map.