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

We study light ray transform of symmetric 2-tensor fields defined on a bounded time-space domain in ${\mathbb{R}}^{1+n}$ for $n\ge 3$. 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.