The Light Ray transform on Lorentzian manifolds

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.

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Cited by in corpus (5)

• The Light Ray transform in Stationary and Static Lorentzian geometries
• Global recovery of a time-dependent coefficient for the wave equation from a single measurement
• Some integral geometry problems for wave equations
• A uniqueness result for light ray transform on symmetric 2-tensor fields
• Scattering rigidity for standard stationary manifolds via timelike geodesics