Determining Lorentzian manifold from non-linear wave observation at a single point

We consider an inverse problem for a non-linear hyperbolic equation. We show that conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evaluated along a single timelike curve. We use the microlocal analysis of non-linear wave interaction.

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Bibliographic Details
Published in:arXiv.org 2023-10
Main Authors: Nursultanov, Medet, Oksanen, Lauri, Tzou, Leo
Format: Article
Language:English
Subjects:
Inverse problems
Manifolds (mathematics)
Wave interaction
Online Access:Get full text
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Description
Summary:We consider an inverse problem for a non-linear hyperbolic equation. We show that conformal structure of a Lorentzian manifold can be determined by the source-to-solution map evaluated along a single timelike curve. We use the microlocal analysis of non-linear wave interaction.
ISSN:2331-8422