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 ray transform Lf by a suitable filtered back-projection.

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Correspondence to Plamen Stefanov.

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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).

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