Singularities are a generic feature of Einstein’s general theory of relativity. Like the Big Bang, singularities may be present at the initial state of our universe, or develop over time when stars collapse, like black holes. Mathematically such situations occur when a solution to the Einstein equations is inextendible beyond a certain point — there is a void in the universe, described by geodesic incompleteness.
The singularity theorems of Penrose and Hawking mathematically describe the occurrence of geodesic incompleteness for Lorentzian metrics which are essentially twice continuously differentiable and satisfy amongst others lower Ricci curvature bounds. In order to study nonsmooth spacetimes, I aim at developing a synthetic theory of lower Ricci curvature bounds in the Lorentzian setting as has already been done successfully in the Riemannian case.
During my stay at ESI my collaborators and I will initiate the study of geometric functional inequalities that likely require lower Ricci curvature bounds, for example derive a Brunn-Minkowski type inequality for smooth Lorentzian manifolds.
For more information on my research please refer to