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.
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ML partly supported by Academy of Finland, Grants 273979, 284715, 312110, 314879 and the AtMath project of UH.
LO partly supported by EPSRC Grant EP/P01593X/1 and EP/R002207/1.
PS partly supported by NSF Grants DMS-1600327 and DMS-1900475.
GU was partly supported by NSF a Walker Family Endowed Professorship at UW ad a Si-Yuan Professorship at HKUST.
Communicated by P. Chrusciel
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Lassas, M., Oksanen, L., Stefanov, P. et al. The Light Ray Transform on Lorentzian Manifolds. Commun. Math. Phys. 377, 1349–1379 (2020). https://doi.org/10.1007/s00220-020-03703-6