We model massive dark objects at centers of many galaxies as Schwarzschild black hole lenses and study gravitational lensing by them in detail. We show that the ratio of mass of a Schwarzschild lens to the differential time delay between outermost two relativistic images (both of them either on the primary or on the secondary image side) is extremely insensitive to changes in the angular source position as well as the lens-source and lens-observer distances. Therefore, this ratio can be used to obtain very accurate values for masses of black holes at centers of galaxies. Similarly, angular separations between any two relativistic images are also extremely insensitive to changes in the angular source position and the lens-source distance. Therefore, with the known value of mass of a black hole, angular separation between two relativistic images would give a very accurate result for the distance of the black hole. Accuracies in determination of masses and distances of black holes would however depend on accuracies in measurements of differential time delays and angular separations between images. Deflection angles of primary and secondary images as well as effective deflection angles of relativistic images on the secondary image side are always positive. However, the effective deflection angles of relativistic images on the primary image side may be positive, zero, or negative depending on the value of angular source position and the ratio of mass of the lens to its distance. We show that effective deflection angles of relativistic images play significant role in analyzing and understanding strong gravitational field lensing.
In this manuscript, we consider the hairy Schwarzschild black hole that evades the no-hair theorem. The hair is induced by an additional source from surroundings, such as dark matter, that has a constant energy-momentum tensor(EMT). We study the strong gravitational lensing of light in the background of the hairy Schwarzschild black hole. We observe that the lensing coefficient $\overline{a}$ increases with $α$ but decreases with $\ell_0$. The opposite effect is observed for the lensing coefficient $\overline{b}$ and the impact parameter $b_m$. We also notice that the angular position $θ_\inft…
We model the supermassive dark object $M87^*$ as a Schwarzschild lens and study the variations in tangential, radial, and total (the product of tangential and radial) magnifications of images (primary, secondary, and relativistic) against the changes in angular source position and the ratio of lens-source to the observer-source distance. Further, we study the behavior of partial derivatives (with respect to the angular source position) of total magnifications of images against the angular source position. Finally, we model supermassive dark objects at centers of 40 galaxies as Schwarzschild le…
Topologically Charged Holonomy corrected Schwarzschild black hole lensing
Instituto Federal de Educação Ciência e Tecnologia do Maranhão（马拉尼昂联邦教育、科学和技术学院）；Faculdade de Física, Universidade Federal do Pará（帕拉联邦大学物理学院）；Departamento de Física e Química, Universidade Federal do Espírito Santo（圣埃斯皮里图联邦大学物理与化学系）
We calculate the photon sphere $r_{ph}$ and critical curve $b_c$ for the quantum corrected Schwarzschild black hole, finding that they violate an universal inequalities proved for asymptotically flat black holes which satisfy null energy condition in the framework of Einstein gravity. This violation seem to be a common phenomenon when considering quantum modification of Einstein gravity. Furthermore, we study the shadows, lensing rings and photon rings in the quantum corrected Schwarzschild black hole. The violation leads to a larger bright lensing ring in the observational appearance of thin …
In this paper, we study the influence of the axion-plasmon, as proposed in (Phys. Rev. Lett. 120, 181803 (2018)) on the optical properties of the Schwarzschild black hole. Our aim is to provide a test to detect the effects of a fixed axion background using black holes. To accomplish our goal, we explore the effect of the axion-plasmon coupling on the motion of photons around the Schwarzschild black hole and check the possibility of observing those effects upon the black hole shadow, the gravitational deflection angle, Einstein rings and shadow images obtained by radially infalling gas on a bla…
In this work, we observe that in the presence of the string cloud parameter $a$ and the quintessence parameter $γ$, with the equation of state parameter $ω_q={-2}/{3}$ the radius of the shadow of the Schwarzschild black hole increases as compared with the pure Schwarzschild black hole case. The existence of both quintessential dark energy and cloud of strings magnify the shadow size and hence the strength of the gravitational field around the Schwarzschild black hole increases. Using the data collected by the Event Horizon Telescope (EHT) collaboration for the M87* and Sgr A*, we obtain upper …
One-loop renormalised quantum effective action for gravity contains quadratic in curvature terms. We have found an approximate analytic black hole solution in quadratic gravity by keeping only the radial spherically symmetric fluctuations and dimensionally reducing the 4-dimensional (4D) theory down to the 2-dimensional (2D) dilaton gravity with a potential. The solution reduces to the Schwarzschild black hole in the limit of Einstein's gravity, but otherwise admits non-negative Arnowitt-Deser-Misner (ADM) and positive quasi-local Misner-Sharp masses that can differ significantly. We then stud…
The light rings (LRs) topological charge (TC) of a spacetime measures the number of stable LRs minus the number of unstable LRs. It is invariant under smooth spacetime deformations obeying fixed boundary conditions. Asymptotically flat equilibrium black holes (BHs) have, generically, TC=$-1$. In Einstein-Maxwell theory, however, the Schwarzschild-Melvin BH - describing a neutral BH immersed in a strong magnetic field - has TC$=0$. This allows the existence of BHs without LRs and produces remarkable phenomenological features, like panoramic shadows. Here we investigate the generalised Schwarzsc…
Plasma impact on black hole shadow and gravitational weak lensing for Schwarzschild-like black hole
Harbin Institute of Technology（哈尔滨工业大学）；University of Tashkent for Applied Sciences（塔什干应用科学大学）；New Uzbekistan University（新乌兹别克斯坦大学）；National University of Uzbekistan（乌兹别克斯坦国立大学）
