Rigidity in the Lorentzian Calderón problem with formally determined data
Year: 2026
Type: article
Abstract: We study the Lorentzian Calderón problem, where the objective is to determine a globally hyperbolic Lorentzian metric up to a boundary fixing diffeomorphism from boundary measurements given by the hyperbolic Dirichlet-to-Neumann map. This problem is a wave equation analogue of the Calderón problem on Riemannian manifolds. We prove that if a globally hyperbolic metric agrees with the Minkowski metric outside a compact set and has the same hyperbolic Dirichlet-to-Neumann map as the Minkowski metric, then it must be the Minkowski metric up to diffeomorphism. In fact this follows from a stronger result that solves a formally determined inverse problem with a much smaller amount of measurements. To prove these results we introduce a new method for geometric hyperbolic inverse problems. The method is based on distorted plane wave solutions and on a combination of geometric, topological and unique continuation arguments.
DOI: 10.1090/cams/73
Authors: Lauri Oksanen, Rakesh, Mikko Salo
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Awards: Hyperbolic Inverse Problems, G2047464261, The inverse backscattering problem and the inverse fixed angle scattering problem, Flagship of Advanced Mathematics for Sensing, Imaging and Modelling, Centre of Excellence of Inverse Modelling and Imaging, G3150356333, Geometric inverse boundary value problems, G3785560064, Centre of Excellence of Inverse Modelling and Imaging, G4824063805, G5144740699, G5578606746, G6050895953, G6421542258, G6501452681, G6518774002, Flagship of Advanced Mathematics for Sensing, Imaging and Modelling, G6966352178, G6974003646, G7074815227, G7129815112, G7561699690, G8137207112, G8599955509
OpenAlex ID: W7166591087