Travel time tomography in stationary spacetimes

2020/08/01 by Günther Uhlmann, Yang Yang, Uhlmann, Gunther +3 · 1 citation
Mathematics · #Algebraic and Geometric Analysis #Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.2008.00347

openalex publication_date 2020/08/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the boundary rigidity problem on a cylindrical domain in \mathbb R¹⁺ⁿ, n≥ 2, equipped with a stationary (time-invariant) Lorentzian metric. We show that the time separation function between pairs of points on the boundary of the cylindrical domain determines the stationary spacetime, up to some time-invariant diffeomorphism, assuming that the metric satisfies some a-priori conditions.

Citations

• Uniqueness of the multi-dimensional inverse scattering problem for time dependent potentials
• On the inverse problem of finding cosmic strings and other topological\n defects
• Inverse problems for Lorentzian manifolds and non-linear hyperbolic\n equations

Cited by

• The Dirichlet-to-Neumann map for Lorentzian Calderón problems with data on disjoint sets

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