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

Mohsen Fathi; Marco Olivares; J. R. Villanueva

doi:10.1140/epjc/s10052-022-10600-w

2021 Impact factor 4.991

Particles and Fields

Open Access

Eur. Phys. J. C (2022) 82: 629
https://doi.org/10.1140/epjc/s10052-022-10600-w

Regular Article - Theoretical Physics

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

Mohsen Fathi¹^a, Marco Olivares² and J. R. Villanueva¹

¹ Instituto de Física y Astronomía, Universidad de Valparaíso, Avenida Gran Bretaña 1111, Valparaiso, Chile
² Facultad de Ingeniería y Ciencias, Universidad Diego Portales, Avenida Ejército Libertador 441, Santiago, Chile

^a mohsen.fathi@postgrado.uv.cl

Received: 14 February 2022
Accepted: 8 July 2022
Published online: 22 July 2022

Abstract

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.

© The Author(s) 2022

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