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

中文翻译：

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从双曲方程的边界数据恢复时间相关系数

我们从双曲方程的狄利克雷到诺依曼映射的知识中研究了黎曼流形上随时间变化的磁矢量值电位和电标量值电位的恢复的唯一性。柯西数据是在时空边界的类时部分上观察到的，唯一性被证明是问题的自然标准。证明基于高斯光束和洛伦兹流形上光线变换的反演，假设洛伦兹流形是黎曼流形与时间间隔的乘积，并且测地线射线变换在黎曼流形上是可逆的。