Gravitational Lensing

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