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We study the determination of the mass of a de Sitter–Schwarzschild black hole from one quasinormal mode. We prove a local uniqueness result with a Hölder type stability estimate. [ABSTRACT FROM AUTHOR]

We study the light ray transform on Minkowski space-time and its small metric perturbations acting on scalar functions which are solutions to wave equations. We show that the light ray transform uniquely determines the function in a stable way. The problem is of particular interest because of its connection to inverse problems of the Sachs–Wolfe effect in cosmology. [ABSTRACT FROM AUTHOR]

We consider inverse problems in space-time (M, g), a 4-dimensional Lorentzian manifold. For semilinear wave equations □gu+H(x,u)=f, where □g denotes the usual Laplace-Beltrami operator, we prove that the source-to-solution map L:f→u|V, where V is a neighborhood of a time-like geodesic μ, 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 μ 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. [ABSTRACT FROM AUTHOR]