Home Page of Roland Steinbauer


A brief description of my research topics

Mathematical General Relativity

Mathematical General Relativity (GR) is concerned with the mathematical study of Albert Einsteins theory of space, time and gravitation, which was established almost exactly 100 years ago. My own research in this area is mostly concerned with questions of low regularity. In fact, the geometric foundation of GR is Lorentzian geometry which is usually formulated in the smooth category. On the other hand, the nature of GR as a physical theory and its analytic foundations (most notably hyperbolic PDE) demand the use of non-smooth functions and regularity issues become essential.

Algebras of generalized functions and applications

Algebras of generalized functions, also known as Colombeau Algebras, are sheaves of differential algebras which contain the vector space of Schwartz distributions as a subspace and the space of smooth functions as a subalgebra, hence provide a framework for multiplying distributions which benefits from maximal compatibility with classical analysis (read more...) In particular, I'm interested in all geometric aspects of this theory and its applications, most of all in general relativity and PDE.

Kinetic theory

I have also done some work in nonlinear PDE, more precisely in collissionless models in kinetic theory. Together with Gerhard Rein, Michael Kunzinger and Gerald Teschl I have studied the Vlasov-Klein-Gordon system: In [P13] we have proven the existence of local weak solutions, while in [P19] we have derived local classical solvability plus a continuation criterion. Again with Michael Kunzinger and Irina Kmit I have studied singular solutions of the Vlaosov-Poisson system ([P22]) with the aim of looking at the singular limits of the VP-system, i.e., the Euler equations and the n-body problem.

Gravitational waves

Quite early in my career I developped some interest in gravitational wave detection, which resulted in two fun-papers [Mi1] and [Mi3] where together with some fellow students as well as Karsten Danzmann we put forward the idea of a space-borne gravitational wave detector much larger than LISA. Of course such a project is not at all feasable.