Reconstruction of Lorentzian Manifolds from Boundary Light Observation Sets

Abstract On a time-oriented Lorentzian manifold (M, g) with nonempty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets S ⊂ M of sources is uniquely determined by measurements of the intersection of future light cones...

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Bibliographic Details
Published in:International mathematics research notices 2019-11, Vol.2019 (22), p.6949-6987
Main Authors: Hintz, Peter, Uhlmann, Gunther
Format: Article
Language:English
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Summary:Abstract On a time-oriented Lorentzian manifold (M, g) with nonempty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets S ⊂ 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 ∂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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnx320