# Gravitational Lensing

### Black Hole Imaging

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## Abstract

A black hole is an object in space where the pull of its gravity is so strong

that no light can escape. This notion gives rise to the phenomenon called

gravitational lensing which is the effect where light is being bent by a massive

object, in our case a black hole. With these two concepts in mind we are

able to formulate the goal of this thesis: we aim to simulate and visualize the

distortion of a projected image caused by the gravitational field of a black

hole.

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 in

reaching that goal. We are then able to create a concrete plan to reach our

goal in manageable consecutive steps.

We find that determining geodesics in a specified metric is one of the most

important 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 which

we solve by means of numerical methods. These results are visualised and

proved 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 Minkowski

space we make a start with actually visualizing the paths of light rays.

We continue to our final metric, the Schwarzschild metric. The Schwarzschild

geometry essentially describes the spacetime geometry of empty space sur-

rounding any spherical mass which in our case will be a black hole. We

calculate and visualize the geodesics thoroughly and created the image con-

structor for the Schwarzschild metric. This image constructor visualises how

an image will be altered by being projected in a Schwarzschild metric with

respect to that image in the Minkowski metric. Once the image constructor

is up and running a significant amount of time is specifically dedicated to

showcasing the constructed images.

We conclude that we have reached our defined goal since we are able to

simulate 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 Physics

and Mathematical theory that had to be understood and applied in order to

create the entire thesis