Integrability of Kerr-Newman spacetime with cloud strings, quintessence and electromagnetic field

TL;DR

This paper demonstrates the integrability of charged particle dynamics around a Kerr-Newman black hole influenced by cloud strings, quintessence, and electromagnetic fields, revealing stable orbits in various planes and the effects of dynamical parameters.

Contribution

It introduces the integrability of particle motion in this complex spacetime and analyzes the existence and stability of various orbits, including nonequatorial and spherical orbits, influenced by multiple parameters.

Findings

Stable circular orbits exist in equatorial and nonequatorial planes.

Numerical evidence of stable and marginally stable spherical orbits.

Presence of stable spherical orbits with zero angular momentum across latitudes.

Abstract

The dynamics of charged particles moving around a Kerr-Newman black hole surrounded by cloud strings, quintessence and electromagnetic field is integrable due to the presence of a fourth constant of motion like the Carter constant. The fourth motion constant and the axial-symmetry of the spacetime give a chance to the existence of radial effective potentials with stable circular orbits in two-dimensional planes, such as the equatorial plane and other nonequatorial planes. They also give a possibility of the presence of radial effective potentials with stable spherical orbits in the three-dimensional space. The dynamical parameters play important roles in changing the graphs of the effective potentials. In addition, variations of these parameters affect the presence or absence of stable circular orbits, innermost stable circular orbits, stable spherical orbits and marginally stable spherical orbits. They also affect the radii of the stable circular or spherical orbits. It is numerically shown that the stable circular orbits and innermost stable circular orbits can exist not only in the equatorial plane but also in the nonequatorial planes. Several stable spherical orbits and marginally stable spherical orbits are numerically confirmed, too. In particular, there are some stable spherical orbits and marginally stable spherical orbits with vanishing angular momenta for covering whole the range of the latitudinal coordinate.