Oscillatory singularities in general relativity

The long term goal of the proposed research is to understand the class of oscillatory and spatially inhomogenous big bang singularities.

This class is expected to include the generic case and is therefore of central importance for understanding singularity formation in general relativity and addressing, e.g., strong cosmic censorship.

Analyzing the corresponding spacetimes is very difficult, and there is only partial understanding even in the spatially homogeneous setting.

In the spatially inhomogeneous setting there are no results, not even an existence proof (of a spatially inhomogeneous oscillatory solution).

The difficulty is due to the fact that the relevant equations are diffeomorphism invariant, that gauge fixing leads to a system of non-linear hyperbolic PDE´s and that the asymptotics are locally expected to be chaotic, exhibit violent spatial variations and to have a complicated causal structure. Trying to obtain an understanding via a stability proof is not a viable option since the model dynamics are chaotic.

The purpose of the project is to take the first steps towards constructing oscillatory and spatially inhomogeneous big bang solutions. This is in itself a very difficult problem, but can be expected to be solvable in the time frame of the project. The long term goal of understanding generic solutions can be expected to take at least 10-20-years to attain.

The main research contribution will be made by the PI in collaboration with a PhD student and a postdoc.