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

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.

Corrected typo in title

References in corpus (4)

• Motion of charged particles near weakly magnetized Schwarzschild black hole
• Superradiant instability of black holes immersed in a magnetic field
• Motion of charged particles around a magnetized/electrified black hole
• Photon capture cones and embedding diagrams of the Ernst spacetime