2022

Liimatainen, Tony; Oksanen, Lauri

We construct counterexamples to inverse problems for the wave operator on domains in Rn+1, n≥2, and on Lorentzian manifolds. We show that non-isometric Lorentzian metrics can lead to same partial data measurements, which are formulated in terms certain restrictions of the Dirichlet-to-Neumann map. The Lorentzian metrics giving counterexamples are time-dependent, but they are smooth and non-degenerate. On Rn+1 the metrics are conformal to the Minkowski metric.