A1 Journal article (refereed)
The Light Ray Transform in Stationary and Static Lorentzian Geometries (2021)

Feizmohammadi, A., Ilmavirta, J., & Oksanen, L. (2021). The Light Ray Transform in Stationary and Static Lorentzian Geometries. Journal of Geometric Analysis, 31(4), 3656-3682. https://doi.org/10.1007/s12220-020-00409-y

JYU authors or editors

Ilmavirta, Joonas

Publication details

All authors or editors: Feizmohammadi, Ali; Ilmavirta, Joonas; Oksanen, Lauri

Journal or series: Journal of Geometric Analysis

ISSN: 1050-6926

eISSN: 1559-002X

Publication year: 2021

Volume: 31

Issue number: 4

Pages range: 3656-3682

Publisher: Springer

Publication country: United States

Publication language: English

DOI: https://doi.org/10.1007/s12220-020-00409-y

Publication open access: Openly available

Publication channel open access: Partially open access channel

Publication is parallel published (JYX): https://jyx.jyu.fi/handle/123456789/68739

Web address of parallel published publication (pre-print): https://arxiv.org/abs/1911.04834

Abstract

Given a Lorentzian manifold, the light ray transform of a function is its integrals along null geodesics. This paper is concerned with the injectivity of the light ray transform on functions and tensors, up to the natural gauge for the problem. First, we study the injectivity of the light ray transform of a scalar function on a globally hyperbolic stationary Lorentzian manifold and prove injectivity holds if either a convex foliation condition is satisfied on a Cauchy surface on the manifold or the manifold is real analytic and null geodesics do not have cut points. Next, we consider the light ray transform on tensor fields of arbitrary rank in the more restrictive class of static Lorentzian manifolds and show that if the geodesic ray transform on tensors defined on the spatial part of the manifold is injective up to the natural gauge, then the light ray transform on tensors is also injective up to its natural gauge. Finally, we provide applications of our results to some inverse problems about recovery of coefficients for hyperbolic partial differential equations from boundary data.

Keywords: inverse problems

Free keywords: inverse problems; light ray transform; wave equation

Fields of science: