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
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
Accepted: 8 July 2022
Published online: 22 July 2022
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
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3. SCOAP3 supports the goals of the International Year of Basic Sciences for Sustainable Development.