The Light Ray Transform on Lorentzian Manifolds

We study the weighted light ray transform L of integrating functions on a Lorentzian manifold over lightlike geodesics. We analyze L as a Fourier Integral Operator and show that if there are no conjugate points, one can recover the spacelike singularities of a function f from its the weighted light...

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Bibliographic Details
Published in:Communications in mathematical physics 2020-07, Vol.377 (2), p.1349-1379
Main Authors: Lassas, Matti, Oksanen, Lauri, Stefanov, Plamen, Uhlmann, Gunther
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Conjugate points
Geodesy
Manifolds (mathematics)
Mathematical and Computational Physics
Mathematical Physics
Operators (mathematics)
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary:We study the weighted light ray transform L of integrating functions on a Lorentzian manifold over lightlike geodesics. We analyze L as a Fourier Integral Operator and show that if there are no conjugate points, one can recover the spacelike singularities of a function f from its the weighted light ray transform Lf by a suitable filtered back-projection.
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-020-03703-6