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The Light Ray Transform on Lorentzian Manifolds

Lassas, M; Oksanen, L; Stefanov, P; Uhlmann, G; (2020) The Light Ray Transform on Lorentzian Manifolds. Communications in Mathematical Physics 10.1007/s00220-020-03703-6. (In press). Green open access

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Abstract

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.

Type: Article
Title: The Light Ray Transform on Lorentzian Manifolds
Open access status: An open access version is available from UCL Discovery
DOI: 10.1007/s00220-020-03703-6
Publisher version: https://doi.org/10.1007/s00220-020-03703-6
Language: English
Additional information: This version is the author accepted manuscript. For information on re-use, please refer to the publisher’s terms and conditions.
Keywords: Science & Technology, Physical Sciences, Physics, Mathematical, Physics, INVERSE PROBLEM, STABLE DETERMINATION, INVISIBILITY, OPERATORS, FIELDS
UCL classification: UCL
UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Maths and Physical Sciences > Dept of Mathematics
URI: https://discovery.ucl.ac.uk/id/eprint/10095829
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