Seeing Through Space Time

Abstract: e consider inverse problems for the Einstein equation with a time-depending metric on a 4-dimensional globally hyperbolic Lorentzian manifold.We formulate the concept of active measurements for relativistic models. Wedo this by coupling Einstein equations with equations for scalar fields.The inverse problem we study is the question of whether the observationsof the solutions of the coupled system in an open subset of the space-time withthe sources supported in this set determines the metric in a larger domain. Tostudy this problem we define the concept of light observation sets and showthat knowledge of these sets determine the conformal class of the metric. Thiscorresponds to passive observations from a distant area of space which is filledby light sources.We will start by considering inverse problems for scalar non-linear hyperbolicequations to explain our method. No previous knowledge of Lorentzian geometryor general relativity will be assumed.This is based on joint work with P. Hinz, Y. Kurylev, M. Lassas, Y. Wangand J. Zhai

analysis of PDEsdynamical systemsfunctional analysisoptimization and controlspectral theory

Audience: general audience

Webinar on PDE and related areas

Series comments: The webinar is organised jointly from IIT-Kanpur, TIFR-CAM,Bangalore, IISER-Pune and IISER-Kolkata.

Zoom Link for the talk will be available on iitk.ac.in/math/weekly-webinar-on-pde-and-related-areas

If you would like to receive webinar announcements(including zoom ID and password to attend the talk), please send a blank email with the subject line "WWOPARA_sub" to pdewebinar@iitk.ac.in. In order to unsubscribe, please send us a blank email with the subject "WWOPARA_unsub".