Bay Area Microlocal Analysis Seminar: Determination of space-time structures from gravitational perturbations

Seminar | November 14 | 4:10-5 p.m. | 736 Evans Hall

 Yiran Wang, Stanford

 Department of Mathematics

We consider inverse problems for the Einstein equations with source fields. The problem we are interested in is to determine space-time structures e.g. topological, differentiable structures of the manifold and the Lorentzian metric, by generating small gravitational perturbations and measuring the responses near a freely falling observer. We discuss some unique determination results for Einstein equations with scalar fields and electromagnetic fields under a microlocal linearization stability condition. A key component of our approach is to analyze the new waves generated from the nonlinear interaction of multiple gravitational waves using microlocal techniques. The talk is based on joint works with M. Lassas and G. Uhlmann.