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.