Microlocal analysis of the light ray transform on globally hyperbolic Lorentzian manifolds

Abstract

For the light ray transform on globally hyperbolic Lorentzian manifolds of dimension $n+1 \geq 3$ acting on compactly supported distributions, we show that the Schwartz kernel of the normal operator is a paired Lagrangian distribution with non-vanishing principal symbols on each Lagrangians. We obtain Sobolev estimates for the light ray transform, and clarify the determination of light-like singularities using the normal operator.