Determination of Space‐Time Structures from Gravitational Perturbations

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 bac...

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Bibliographic Details
Published in:Communications on pure and applied mathematics 2020-06, Vol.73 (6), p.1315-1367
Main Authors: Uhlmann, Gunther, Wang, Yiran
Format: Article
Language:English
Subjects:
Einstein equations
Electromagnetic fields
Gravitation
Inverse problems
Mathematical analysis
Maxwell's equations
Scalars
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Summary: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). © 2019 Wiley Periodicals, Inc.
ISSN:0010-3640
1097-0312
DOI:10.1002/cpa.21882