Broken causal lens rigidity: Reconstructing Lorentzian manifolds from geodesic data

Details

Written by Eric Larsson

Lens rigidity problems concern reconstructing a manifold from data about its geodesics. These and similar problems have been extensively studied for Riemannian manifolds, but there are not as many results for Lorentzian manifolds.
I will speak about the following problem: Suppose that we wish to determine the topology, smooth structure and metric of a Lorentzian manifold with boundary, and suppose that we are allowed to send in probes which follow timelike geodesics and which broadcast their proper time along lightlike geodesics. Can we determine the manifold up to isometry by observing these signals at the boundary? I will discuss a method of solving this and similar problems. One of the features of the method is that it does not require an explicit construction of coordinates.