Print Email Facebook Twitter Gravitational Lensing Title Gravitational Lensing: Black Hole Imaging Author Kleynen, Wouter (TU Delft Electrical Engineering, Mathematics and Computer Science; TU Delft Mathematical Physics) Contributor Visser, P.M. (mentor) Hart, K.P. (graduation committee) Degree granting institution Delft University of Technology Programme Applied Mathematics Date 2021-05-03 Abstract A black hole is an object in space where the pull of its gravity is so strongthat no light can escape. This notion gives rise to the phenomenon calledgravitational lensing which is the effect where light is being bent by a massiveobject, in our case a black hole. With these two concepts in mind we areable to formulate the goal of this thesis: we aim to simulate and visualize thedistortion of a projected image caused by the gravitational field of a blackhole.First of all we need to cover the relevant Physics to form some sort of under-standing of the bigger picture and have an idea of all the factors involved inreaching that goal. We are then able to create a concrete plan to reach ourgoal in manageable consecutive steps.We find that determining geodesics in a specified metric is one of the mostimportant factors of this plan. In order to do so we derive the geodesic equa-tion which enables us to calculate these geodesics.We continue by first applying the geodesic equation in two-dimensional Eu-clidean space. This provides us with a system of differential equation whichwe solve by means of numerical methods. These results are visualised andproved to be correct.We then move over to four-dimensional Minkowski space where we calcu-lated and visualised the geodesics for this specific metric. In the Minkowskispace we make a start with actually visualizing the paths of light rays.We continue to our final metric, the Schwarzschild metric. The Schwarzschildgeometry essentially describes the spacetime geometry of empty space sur-rounding any spherical mass which in our case will be a black hole. Wecalculate and visualize the geodesics thoroughly and created the image con-structor for the Schwarzschild metric. This image constructor visualises howan image will be altered by being projected in a Schwarzschild metric withrespect to that image in the Minkowski metric. Once the image constructoris up and running a significant amount of time is specifically dedicated toshowcasing the constructed images.We conclude that we have reached our defined goal since we are able tosimulate and construct the projected images. We look back at all the steps that played a key role in this process.Besides the goal, we spent some time reflecting at all the unfamiliar Physicsand Mathematical theory that had to be understood and applied in order tocreate the entire thesis Subject Black HolesGravitational lensingdifferential geometrygeodesicpythonProgrammingnumerical analysis To reference this document use: http://resolver.tudelft.nl/uuid:a3db6582-2aee-49b1-a616-cf85f29f3409 Bibliographical note https://github.com/WouterKleynen/BEP_software Here you can find all the software I created. Part of collection Student theses Document type bachelor thesis Rights © 2021 Wouter Kleynen Files PDF Gravitational_Lensing_Bla ... maging.pdf 7.11 MB Close viewer /islandora/object/uuid:a3db6582-2aee-49b1-a616-cf85f29f3409/datastream/OBJ/view