Speaker
Description
The singularity theorems of General Relativity (GR) are considered among
the most relevant works in mathematical physics of the last century. They form a body of important results in Lorentzian differential geometry that establishes the occurrence of spacetime ``singularities", in the sense of causal geodesic incompleteness of the spacetime manifold under certain physically reasonable conditions. The most relevant of them are the ones proved by Roger Penrose and Stephen Hawking in the 1960-ies. These results were formulated for smooth spacetimes, however for the theorems to make physically meaningful predictions, one needs to extend their validity to spacetime metrics of low regularity. Already Hawking and Ellis in their book considered the issue of a lack of low regularity version of the theorems, i.e. for spacetime metrics below the $C^2$-class. In recent years there have been efforts in finding low regularity versions of the singularity theorems, getting as low as Lipschitz Lorentzian metrics. The main goal of my research is lowering the regularity threshold to H\"older continuous metrics with $L^p$ bounded curvature. To reach this goal we make use of the RT-equations, elliptic equations whose solution describe the coordinate transformations regularizing connections to one derivative above its curvature, enabling us to apply methods a priori only available for more regular metrics.
Affiliation
Universität Wien