Determination of space-time structures from gravitational perturbations
Analysis of PDEs
2018-06-19 v1
Abstract
We study inverse problems for the Einstein equations with source fields in a general form. Under a microlocal linearization stability condition, we show that by generating small gravitational perturbations and measuring the responses near a freely falling observer, one can uniquely determine the background Lorentzian metric up to isometries in a region where the gravitational perturbations can travel to and return. We apply the result to two concrete examples when the source fields are scalar fields (i.e. Einstein-scalar field equations) and electromagnetic fields (i.e. Einstein-Maxwell equations).
Cite
@article{arxiv.1806.06461,
title = {Determination of space-time structures from gravitational perturbations},
author = {Gunther Uhlmann and Yiran Wang},
journal= {arXiv preprint arXiv:1806.06461},
year = {2018}
}