A uniqueness result for light ray transform on symmetric 2-tensor fields

TL;DR

This paper establishes a uniqueness theorem for the light ray transform of symmetric 2-tensor fields in a bounded spacetime domain, characterizing the kernel near fixed directions, which advances the understanding of tensor tomography in mathematical physics.

Contribution

It provides the first characterization of the kernel of the light ray transform for symmetric 2-tensor fields in a bounded domain, extending previous results in tensor tomography.

Findings

Kernel of the light ray transform characterized near fixed directions

Uniqueness result for symmetric 2-tensor fields in bounded domains

Advances in tensor tomography and inverse problems

Abstract

We study light ray transform of symmetric 2-tensor fields defined on a bounded time-space domain in $\mathbb{R}^{1+n}$ for $n\geq 3$. We prove a uniqueness result for such light ray transforms. More precisely, we characterize the kernel of the light ray transform vanishing near a fixed direction at each point in the time-space domain.