Lassas, Matti; Uhlmann, Gunther; Wang, Yiran
(2018)
We consider inverse problems in space-time (M, g), a 4-dimensional Lorentzian manifold. For semilinear wave equations square(g)u + H (x, u) = f, where square(g) denotes the usual Laplace-Beltrami operator, we prove that the source-to-solution map , L : f -> u broken vertical bar v, where V is a neighborhood of a time-like geodesic mu, determines the topological, differentiable structure and the conformal class of the metric of the space-time in the maximal set, where waves can propagate from mu and return back. Moreover, on a given space-time (M, g), the source-to-solution map determines some coefficients of the Taylor expansion of H in u.