Inverse Problems in General Relativity
Peter Hintz (ETH Zürich, Switzerland)
The main object in general relativity is a spacetime: a manifold equipped with a metric tensor of indefinite signature (n,1). The metric tensor allows one to describe the trajectories of massless particles such as photons and of freely falling massive observers. It also enables one to pose linear and nonlinear wave equations on the spacetime. General relativity thus provides a fertile ground for geometric inverse problems as well as for inverse problems for (non)linear wave equations. The basic question is: can one recover a part of the spacetime from faraway measurements of photons, gravitational waves, or nonlinear waves?
I will begin my talk with an introduction to general relativity, followed by a description of the various types of inverse problems that have been studied in the past decade and a selection of results.