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Determination of Space‐Time Structures from Gravitational Perturbations
Author(s) -
Uhlmann Gunther,
Wang Yiran
Publication year - 2020
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21882
Subject(s) - linearization , gravitational field , einstein , gravitation , mathematics , observer (physics) , scalar (mathematics) , linearized gravity , spacetime , physics , scalar field , electromagnetic field , classical mechanics , metric (unit) , stability (learning theory) , mathematical analysis , mathematical physics , nonlinear system , geometry , computer science , quantum mechanics , operations management , machine learning , economics
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.