Strong gravitational lensing by and black holes embedded in dark matter halo exhibiting string cloud and quintessential field

Niyaz Uddin Molla; Himanshu Chaudhary; G. Mustafa; Farruh Atamurotov; Ujjal Debnath; Dhruv Arora

doi:10.1140/epjc/s10052-024-12917-0

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2024) 84: 574
https://doi.org/10.1140/epjc/s10052-024-12917-0

Regular Article - Theoretical Physics

Strong gravitational lensing by $S g r A^{}$ and $M 87^{}$ black holes embedded in dark matter halo exhibiting string cloud and quintessential field

Niyaz Uddin Molla¹, Himanshu Chaudhary²^,3^,4, G. Mustafa⁵^c, Farruh Atamurotov⁶^,7^,8, Ujjal Debnath¹ and Dhruv Arora³

¹ Department of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, 711 103, Howrah, India
² Department of Applied Mathematics, Delhi Technological University, 110042, Delhi, India
³ Pacif Institute of Cosmology and Selfology (PICS), Sagara, 768224, Sambalpur, Odisha, India
⁴ Department of Mathematics, Shyamlal College, University of Delhi, 110032, Delhi, India
⁵ Department of Physics, Zhejiang Normal University, 321004, Jinhua, People’s Republic of China
⁶ New Uzbekistan University, Movarounnahr Street 1, 100000, Tashkent, Uzbekistan
⁷ University of Tashkent for Applied Sciences, Str. Gavhar 1, 100149, Tashkent, Uzbekistan
⁸ Institute of Theoretical Physics, National University of Uzbekistan, 100174, Tashkent, Uzbekistan

^c gmustafa3828@gmail.com

Received: 18 March 2024
Accepted: 13 May 2024
Published online: 5 June 2024

Abstract

We investigate the strong gravitational lensing phenomena caused by a black hole with a dark matter halo in the presence of cloud string and quintessence. This study examines strong gravitational lensing with two significant dark matter models: the universal rotation curve model and the cold dark matter model. To do this, we first numerically estimate the strong lensing coefficients and strong deflection angles for both the universal rotation curve and cold dark matter models. It is observed that the deflection angle, denoted as $α_{D}$ $\alpha _D$ , increases with the parameter $α$ $\alpha$ while holding the value of $2 M γ$ $2M \gamma$ constant. Additionally, it increases with the parameter $2 M γ$ $2M \gamma$ while keeping the value of $α$ $\alpha$ constant. The strong deflection angle $α_{D}$ $\alpha _D$ , for the black hole with a dark matter halo, with parameters $α$ $\alpha$ and $2 M γ$ $2\,M \gamma$ , greatly enhances the gravitational bending effect and surpasses the corresponding case of the standard Schwarzschild black hole ( $A = B = 0 = α = 2 M γ$ $A=B=0=\alpha =2M\gamma$ ). Furthermore, we investigate the astrophysical consequences through strong gravitational lensing observations, using examples of two supermassive black holes, namely $M 87^{*}$ $M87^{*}$ and $S g r A^{*}$ $Sgr A^{*}$ , located at the center of nearby galaxies. It is observed that black holes with dark matter halos in the presence of cloud string and quintessence can be quantitatively distinguished and characterized from the standard Schwarzschild black hole ( $A = B = 0 = α = 2 M γ$ $A=B=0=\alpha =2M\gamma$ ). The findings in our analysis suggest that observational tests for black holes influenced by dark matter halos, cloud string and quintessence are indeed feasible and viable.

© The Author(s) 2024

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/.