Inverse problems for non-linear wave equations and the Einstein equations
We consider inverse problem for a non-linear wave equation with a time-depending metric tensor on manifolds. In addition, we study the question, do the observation of the solutions of coupled Einstein equations and matter field equations in an open subset U of the space-time M corresponding to sources supported in U determine the properties of the metric in a larger domain W⊂M containing U.
To study these problems we define the concept of light observation sets and show that these sets determine the conformal class of the metric.
The results have been done in collaboration with Yaroslav Kurylev and Gunther Uhlmann.