Recovery of time-dependent coefficients from boundary data for hyperbolic equations

We study uniqueness of the recovery a time-dependent magnetic vector-valued potential and an electric scalar-valued on Riemannian manifold from knowledge Dirichlet to Neumann map hyperbolic equation. The Cauchy data is observed time-like parts space-time boundary proved up natural gauge for problem. proof based Gaussian beams inversion light ray transform Lorentzian manifolds under assumptions that product with time interval geodesic invertible manifold.