Null Geodesics and Strong Field Gravitational Lensing of Black Hole with Global Monopole

Hindawi Publishing Corporation Advances in High Energy Physics Volume 2015, Article ID 854264, 11 pages http://dx.doi.org/10.1155/2015/854264 Research Article Null Geodesics and Strong Field Gravitational Lensing of Black Hole with Global Monopole M. Sharif1 and Sehrish Iftikhar1,2 1 Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore 54590, Pakistan Department of Mathematics, Lahore College for Women University, Lahore 54000, Pakistan 2 Correspondence should be addressed to M. Sharif; Received 16 July 2015; Revised 6 August 2015; Accepted 17 August 2015 Academic Editor: Rong-Gen Cai Copyright © 2015 M. Sharif and S. Iftikhar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The publication of this article was funded by SCOAP3 . We study two interesting features of a black hole with an ordinary as well as phantom global monopole. Firstly, we investigate null geodesics which imply unstable orbital motion of particles for both cases. Secondly, we evaluate deflection angle in strong field regime. We then find Einstein rings, magnifications, and observables of the relativistic images for supermassive black hole at the center of galaxy NGC4486B. We also examine time delays for different galaxies and present our results numerically. It is found that the deflection angle for ordinary/phantom global monopole is greater/smaller than that of Schwarzschild black hole. In strong field limit, the remaining properties of these black holes are quite different from the Schwarzschild black hole. 1. Introduction Geodesics are associated with the motion of free particles traveling along their trajectories whose nature depends upon the spacetime. There are two types of geodesics followed by physical particles, that is, timelike and null (light-like), related to the propagation of massive and massless particles. The study of motion of massless particles such as photons is important from both astrophysical and theoretical points of view. It has been observed that light path is affected by gravity which means that path of a photon through spacetime may be bent by the gravitational field of a massive object such as a star or black hole (BH). The dynamics of test particle not only helps to understand geometrical structure of spacetime but also explains high energy phenomenon occurring near BH such as accretion disks where particles move in circular orbits and formation of jets in which particles escape. Chandrasekhar [1] was the pioneer to investigate geodesic motion of a test particle around Schwarzschild, ReissnerNordström (RN), and Kerr BHs. Fernando et al. [2] constructed geodesic structure of static charged BHs of dilaton gravity and studied orbital motion of test particles. Konoplya [3] analyzed motion of both massless and massive particles around magnetized BHs and concluded that tidal force has considerable effect on the motion of test particles. Leiva et al. [4] studied geodesics of the Schwarzschild BH in rainbow gravity and found that geodesics remain unchanged under the influence of semiclassical effects. Guha and Bhattacharya [5] determined that the null geodesics of five-dimensional RN anti-de Sitter BH have a unique fixed point and are terminating orbits. Pradhan [6] found conditions for the existence of ISCO (inner most stable circular orbit), marginally bound circular orbit, and null circular geodesics in equatorial plane for Kerr-Newman-Taub-NUT BH. Deflection of light in gravitational field around a massive object is referred to as gravitational lensing and an object causing deflection is called gravitational lens. Gravitational lensing is a powerful tool in cosmology as well as in astrophysics to understand distribution of mass in the large scale structures of the universe as well as cluster of galaxies and halos. It provides a useful way to estimate Hubble parameter and detection of dark mater, dark energy, exoplanet, gravitational waves, and so forth. This phenomenon is divided into two regimes: weak and strong lensing. Weak gravitational lensing produces weakly distorted images of the source. In this case, the gravitational lens is not strong enough to form 2 multiple images and high magnification. It helps in the measurement of distribution of luminous as well as dark matter in the universe. If the lens is massive enough and the source and lens are highly aligned, then multiple images are formed from the background source. This phenomenon is known as strong gravitational lensing. The distortion and position of such multiple images carry important information about distribution of mass in faraway galaxies and background sources at large distance. The theory of gravitational lensing was initially developed in weak field approximation but this approach cannot describe the phenomena like high bending of light rays and formation of infinite series of images. This motivates studying the strong gravitational lensing, which not only helps to understand these phenomena but also explains the winding of light rays multiple times around a massive object before reaching to the observer. After the pioneer work of Darwin [7], much work has been done in the context of gravitational lensing in strong field [8–11]. Virbhadra and Ellis [12] studied strong field gravitational lensing of Schwarzschild BH and found a sequence of relativistic images on both sides of optical axis due to large deflection of light near the photon sphere. Frittelli et al. [13] proposed an exact thin-lens equation whose accuracy was shown in the strong field. Bozza [14] developed a useful technique for spherically symmetric BHs in strong field by expanding the deflection angle near the photon sphere. The image detection for low mass BHs is difficult but the supermassive BHs such as Sgr 𝐴∗ are an interesting example of deflection of light in strong field [15, 16]. Ding et al. [17] considered noncommutative BH as gravitational lens and found effect of noncommutative parameter similar to charge by comparing with RN BH. Deng [18] studied gravitational lensing of magnetically charged RN BH pierced by a cosmic string in strong field and found increase in the deflection angle. Sahu et al. [19] showed that strong gravitational lensing can be used to distinguish BHs from naked singularities. Wei et al. [20] explored strong lensing of Kerr-Taub-NUT BH and found significant effect of NUT charge. Different authors [21– 29] studied gravitational lensing of many other astrophysical spacetimes in strong field limit. The fact that the universe is in the phase of accelerating expansion is a major turning point in cosmology which indicates the existence of dark energy supported by several observational evidences. Dark energy is an elusive force having large negative pressure. To understand its exact nature, several dynamical mode (...truncated)