A Uniqueness Result for Light Ray Transform on Symmetric 2-Tensor Fields

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.

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The Light Ray Transform in Stationary and Static Lorentzian Geometries

Feizmohammadi

Ilmavirta

Oksanen

2020

J Geom Anal

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A Fourier approach to tomographic reconstruction of tensor fields in the plane

Omogbhe

2025

Journal of Mathematical Analysis and Applications

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Inversion of the exponential X-ray transform of symmetric 2-tensors

Omogbhe

2024

Applicable Analysis

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A Uniqueness Result for Light Ray Transform on Symmetric 2-Tensor Fields

Cited by 3 publications

References 20 publications

The Light Ray Transform in Stationary and Static Lorentzian Geometries

The Light Ray Transform in Stationary and Static Lorentzian Geometries

A Fourier approach to tomographic reconstruction of tensor fields in the plane

Inversion of the exponential X-ray transform of symmetric 2-tensors

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