Recovery of non-smooth coefficients appearing in anisotropic wave equations

We study the problem of unique recovery of a non-smooth one-form $\mathcal{A}$ and a scalar function $q$ from the Dirichlet to Neumann map, $\Lambda_{\mathcal A,q}$,ofahyperbolicequationonaRiemannianmanifold$(M,g)$. We prove uniqueness of the one-form $\mathcal{A}$ up to the natural gauge, under weak regularity conditions on $\mathcal{A},q$ and under the assumption that $(M,g)$ is simple. Under an additional regularity assumption, we also derive uniqueness of the scalar function $q$. The proof is based on the geometric optic construction and inversion of the light ray transform extended as a Fourier Integral Operator to non-smooth parameters and functions.