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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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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container_title Communications in mathematical physics
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description 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.
doi_str_mv 10.1007/s00220-020-03703-6
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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
title The Light Ray Transform on Lorentzian Manifolds
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