Semiglobal uniqueness for the Lorentzian Calder\'on problem

Abstract

We prove uniqueness in the Lorentzian Calder\'on problem in a semiglobal setting, comparing a potentially large perturbation of the Minkowski metric against a small one. Our proof uses a reduced amount of data, solving a formally determined version of the problem. In contrast to traditional approaches, it employs neither control-theoretic arguments nor a reduction to a geometric inverse problem via microlocal methods or high-frequency solutions. Instead, it relies on distorted plane waves and weighted $L^2$-estimates.