Physics Projects

Activities in Analytical Mechanics (german)

This is a loose collection of independent activities in classical mechanics, special relativity, as well as Lagrangian and Hamiltonian mechanics. Each activity is provided with solutions, further comments and fitting literature.

The activities were create as part of my exercise class for the lecture Allgemeine Mechanik held by Prof. Dr. Renato Renner (institute of Theoretical Physics, ETH Zurich, Switzerland) in the fall semester of 2021.

For more information, see the german version of this page.

ETH Semester Project on the Shadow of a Rotating Black Hole

In the last semester (spring 2021) of my BSc physics at ETH Zürich, I wrote a semester project in theoretical physics on the shadow of rotating black holes. The shadow of a black hole is the completely black area in the sky an observer sees when looking at an unobstructed black hole; the shape and size depends on the properties of the black hole and can even be used to infer some of these properties. The project is a literature review of fundamental as well as recent research in the field. As such, it can serve as a structured introduction to the field of black hole shadows.

Title: The Shadow of a Rotating Black Hole

Prof. Dr. Philippe Jetzer (main supervisor), Physik-Institut, University of Zürich, Switzerland
Prof. Dr. Renato Renner (internal ETH member), Institute of Theoretical Physics, ETH Zürich, Switzerland

The aim of this work is to provide an introduction to the field of shadows of rotating Kerr black holes. We review the mathematics of light propagation in Kerr spacetime and derive the equations describing the edge of a Kerr black hole shadow in the sky of a distant observer. We also discuss recent research concerning the possibility of determining the spin parameter a and the inclination angle θO of the observer from direct observations of the shadow. Finally, we showcase two applications of the theory of black hole shadows to the Event Horizon Telescope collaboration image of the supermassive black hole M87*.

PDF file: PDF logosemester project
The project can also be found on the webpage of Prof. Jetzer's research group: here.

Kerr shadows
The shadow edge of various rotating black holes (colours distinguish spin parameters, green is zero, red is maximal), seen from various inclination angles θO. This is fig. 3 of the semester project.

cuRRay - CUDA Relativistic Raytracer

cuRRay is an acronym for CUDA relativistic raytracer, a software I programmed. The software calculates the trajectories of light particles, that is, light rays, near black holes. This way, images of objects near these cosmological monsters can be created. According to Einstein's theory of general relativity, light rays are deflected by the extreme gravity of black holes. The curved light rays lead to highly distorted images of the objects. cuRRay uses NVIDIA CUDA to efficiently compute the paths of light using the graphics card.

cuRRay is the software I programmed for my Matura project at my former high school, Kantonsschule Wohlen. The project won two main prizes at the 2018 swiss national contest of Schweizer Jugend Forscht (SJF): Firstly, a participation at the Stockholm International Youth Science Seminar (SIYSS) 2018, a week-long programme in the context of the Nobel prizes in Stockholm, Sweden. Secondly, a participation at the 2018 European Union Contest for Young Scientists (EUCYS) in Dublin, Ireland. There the project won a special price offered by the European Southern Observatory (ESO) allowing me to travel to Chile and visit telescopes and research sites of ESO. As a hobby astrophotographer, I particularely enjoyed this amazing trip.

You can find more information on cuRRay here.

GitLab logocuRRay at GitLab

Three images created by cuRRay. A black hole (black ball) with a ring (green-gray checkerboard pattern on one side, magenta-gray pattern on the other) is shown from three different angles: top-down, from diagonally above and from slightly above the equator.


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