Support theorems for the Light Ray transform on analytic Lorentzian manifolds

TL;DR

This paper proves support theorems for the light ray transform on analytic Lorentzian manifolds, showing how functions can be recovered from integrals over lightlike geodesics under certain conditions.

Contribution

It establishes new support theorems for the weighted light ray transform on analytic Lorentzian manifolds, extending previous results to this geometric setting.

Findings

Support theorems proven for weighted light ray transform

Results hold for analytic Lorentzian manifolds and weights

Enhances understanding of inverse problems in Lorentzian geometry

Abstract

We study the weighted ray transform of integrating functions on a Lorentzian manifold over lightlike geodesics. We prove support theorems if the manifold and the weight are analytic.