Reconstruction of Lorentzian manifolds from boundary light observation sets

Abstract

On a time-oriented Lorentzian manifold $(M,g)$ with non-empty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets $S\subset M$ of sources is uniquely determined by measurements of the intersection of future light cones from points in $S$ with a fixed open subset of the boundary of $M$; here, light rays are reflected at $\partial M$ according to Snell's law. Our proof is constructive, and allows for interior conjugate points as well as multiply reflected and self-intersecting light cones.

34 pages, 11 figures. v2 is the published version, with typos fixed

References in corpus (4)

• Determination of vacuum space-times from the Einstein-Maxwell equations
• Inverse problems in spacetime I: Inverse problems for Einstein equations - Extended preprint version
• Inverse problems for semilinear wave equations on Lorentzian manifolds
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• Inverse problems for non-linear hyperbolic equations with disjoint sources and receivers
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• An inverse boundary value problem for a semilinear wave equation on Lorentzian manifolds
• Scattering rigidity for standard stationary manifolds via timelike geodesics