Study of null and time-like geodesics in the exterior of a Schwarzschild black hole with quintessence and cloud of strings

• Published in: The European physical journal. C, Particles and fields Vol. 82; no. 7; pp. 1 - 17
• Main Authors: Fathi, Mohsen, Olivares, Marco, Villanueva, J. R.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-07-2022; Springer; Springer Nature B.V; SpringerOpen
• Subjects: Astronomy; Astrophysics and Cosmology; Black holes; Circular orbits; Dark matter; Elementary Particles; Elliptic functions; Equations of motion; Exact solutions; Geodesy; Gravitational waves; Gravity; Hadrons; Heavy Ions; Investigations; Measurement Science and Instrumentation; Nuclear Energy; Nuclear Physics; Orbits; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quintessence (cosmology); Regular Article - Theoretical Physics; Spacetime; String Theory; Theory of relativity; Universe
• ISSN: 1434-6052; 1434-6044; 1434-6052
• DOI: 10.1140/epjc/s10052-022-10600-w

Recently, an analytical study of radial and circular orbits for null and time-like geodesics that propagate in the spacetime produced by a Schwarzschild black hole associated with cloud of strings, in a universe filled by quintessence, has been done in Mustafa and Hussain (Eur Phys J C 81:419, 2021). In this paper, we complete the aforementioned study by investigating possible analytical solutions to the equations of motion for other types of bound orbits, beside taking into account the cases of unbound orbits. This requires an extensive study of the corresponding effective potentials that categorize the test particle motion. We follow the standard Lagrangian dynamics to parametrize the radial and angular geodesics and the resultant (hyper-)elliptic integrals of motion are treated accordingly. We also simulate the orbits which correspond to different levels of energy in the effective potentials.