# The Light Ray transform on Lorentzian manifolds

## TL;DR

This paper investigates the weighted light ray transform on Lorentzian manifolds, demonstrating that under certain conditions, spacelike singularities of functions can be reconstructed from light ray data using Fourier Integral Operator analysis.

## Contribution

It introduces a Fourier Integral Operator framework for the light ray transform on Lorentzian manifolds and establishes conditions for reconstructing spacelike singularities.

## Key findings

- Reconstruction of spacelike singularities is possible without conjugate points.
- The light ray transform can be analyzed as a Fourier Integral Operator.
- Filtered back-projection enables recovery of function singularities.

## 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.