Maximilian’s research lies within the framework of kinetic theory, where he considers certain meta models which consist of ensembles of particles that all look alike. These models play a role in several different fields in physics, such as plasma physics. But the particles can also, as in Maximilian’s work, signify stars, galaxies and galaxy clusters – it is just a matter of different scales. The particles interact with different forces, such as an electromagnetic field in plasma and a gravitational field in a galaxy. Maximilian investigates the interaction in gravitational fields, i.e. what happens with the particles – if they form time-independent clouds, if they collapse into dense objects, or if they disperse.
The Einstein-Vlasov system
There are two common ways to describe gravity. The oldest and simplest is the Newtonian, but often it is not accurate enough. In Maximilian’s work, the particles do not collide but they “feel” the gravitational field created by all the particles collectively. This is described by the Vlasov equation, which is coupled to Einstein’s theory of General Relativity. Gravity is not seen as a force, but as a curvature of the spacetime that the particles live in. The motivation for using this theory instead is that it can describe astronomical objects like galaxies and galaxy clusters very well. In some contexts the difference is not so big, but certain circumstances need new mechanisms, like when the behaviour of the particles is very different from the usual. Examples are very dense particle clouds, or models of the universe as a whole, allowing for the study of its expansion behaviour.
The thesis consists of two parts. The first involves steady states, where time independent clouds of particles like globular clusters too small to be called galaxies are studied as regarding what symmetries they have and how dense they can be. The other part is about small data time evolution, what happens if we only have a few particles scattered around? In space, there is no perfect vacuum, there are always some particles and there are stability questions regarding these – do they for example clump together? Maximilian’s thesis show that the particles move away into infinity and that vacuum space time is stable. There are many others working with these questions through testing different meta models, but the Vlasov model is more complex and more reliable than most.
Collaboration led to PhD position
That Maximilian ended up doing his PhD thesis in Gothenburg is something of a coincidence. He has a physicist background from Constance and was working with similar things in Vienna, where he had a collaboration with Håkan Andréasson, his future supervisor. Håkan suggested that Maximilian should apply for a still vacant PhD position which had not been appointed in the usual admission during Spring, and so he did. Since he was not a Mathematician he had to prove himself and also catch up with courses during his PhD time. In Gothenburg the PhD students read rather many courses compared to other places, but that suited Maximilian’s situation well.
– I have had good conditions here, for example I have had the possibility of two stays abroad, each for three months. You are very free as a PhD student in Sweden, which is good as you can follow your research interest, but there can also be difficulties in being certain of what is a good research question and what the relevant methods are. If I had been working more closely to my supervisor all the time I would probably also have had fewer other research contacts than today.
After the thesis defence, Maximilian plans to try a different work environment through going to Munich and the private industry. Something with simulations or maybe the financial sector are two options, where mathematical methods as wave equations and geometry can be used.
Maximilian Thaller will defend his PhD thesis “On the Einstein-Vlasov system with massless or charged particles: stationary and small data solutions” on January 24 at 10.15 in the room Pascal, Hörsalsvägen 1. Supervisor is Håkan Andréasson.
Text and photo: Setta Aspström