Citation: Javed, W.; Riaz, S.; Övgün, A. Weak Deflection Angle and Greybody Bound of Magnetized Regular Black Hole. Universe 2022, 8, 262. https://doi.org/10.3390/ universe8050262 Academic Editors: Sunny Vagnozzi, Eleonora Di Valentino, Alessandro Melchiorri, Olga Mena, Luca Visinelli and Yi-Fu Cai Received: 11 March 2022 Accepted: 22 April 2022 Published: 25 April 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). universe Article Weak Deflection Angle and Greybody Bound of Magnetized Regular Black Hole Wajiha Javed 1,† , Sibgha Riaz 1,† and Ali Övgün 2, * ,† 1 Department of Mathematics, Division of Science and Technology, University of Education, Township Campus, Lahore 54590, Pakistan; wajiha.javed@ue.edu.pk (W.J.); sibghariaz993@gmail.com (S.R.) 2 Physics Department, Eastern Mediterranean University, North Cyprus via Mersin 10, Famagusta 99628, Turkey * Correspondence: ali.ovgun@emu.edu.tr † These authors contributed equally to this work. Abstract: In this paper, we examine the weak deflection angle and greybody bound for a magnetized regular black hole. For this purpose, we apply the Gauss–Bonnet theorem on the black hole and obtain the deflection angle in plasma and non-plasma mediums. Moreover, we investigate graphically the effect of impact parameter on the deflection angle for regular black hole in both mediums. We examine that the deflection angle goes to infinity when the impact parameter approaches zero. We also observe that the deflection angle shows negative behaviour at q = 0.6 and q = 2.09, but at 0.6 < q < 2.09, the angle shows positive behaviour. Furthermore, we study the rigorous bound phenomenon of the greybody factor in the background for a magnetized regular black hole. Later, we analyse the graphical behaviour of greybody bound with respect to different values of ω and observe that, at small values of ω, the bound increases, but for large values, the bound decreases. After that, we examine that, when we put G = 1, l = 0 and q = 0, all results for the magnetized regular black hole solution reduce into results of the Schwarzschild black hole solution. Keywords: general relativity; gravitational lensing; magnetized black holes; Gauss–Bonnet theorem; plasma medium; greybody factory PACS: 95.30.Sf; 98.62.Sb; 97.60.Lf 1. Introduction Black holes—a great prediction of Einstein’s theory of general relativity (GR) and, at the same time, the understandable objects inside the universe—are of the utmost importance for classical and quantum gravity theories [1]. A region of space having such a strong gravitational field that matter or radiation, even light, cannot escape from it, is called a black hole (BH). Initially BHs were known as “Collapser”, the term derived from the collapse of a star; later, Wheeler put forward the term black hole [2]. A BH is an important tool for examining and testing the fundamental laws of the universe. In fact, the Event Horizon Telescope collaboration captured the first image of a BH [3]. In 1916, Einstein anticipated the existence of gravitational lensing (GL) and gravita- tional waves as part of the basics behind GR [1]. Recently, the gravitational waves were detected by the Laser Interferometer Gravitational Wave Observatory (LIGO) in 2015, which indicated that the theoretical predictions were well expressed with experimental observations [4]. After the detection of gravitational waves, a wide range of gravity theories faced many drawbacks, but the discovery of gravitational waves has gained interest in the field of GL [5]. As the light emitted by distant galaxies passes by massive objects in the universe, the gravitational pull from these objects can distort or bend the light. This is called gravitational lensing. Gravitational lensing is a helpful method to understand dark matter, galaxies, and the universe. Universe 2022, 8, 262. https://doi.org/10.3390/universe8050262 https://www.mdpi.com/journal/universe