On the light ray transform of wave equation solutions

TL;DR

This paper investigates the light ray transform on Minkowski space-time and its perturbations, demonstrating that it uniquely and stably determines solutions to wave equations, with implications for cosmological inverse problems.

Contribution

It establishes the unique and stable recovery of wave equation solutions from the light ray transform on Minkowski space-time and perturbations, linking to cosmological inverse problems.

Findings

Light ray transform uniquely determines wave solutions.

Stable reconstruction is possible from the transform.

Applications to inverse problems in cosmology.

Abstract

We study the light ray transform on Minkowski space-time and its small metric perturbations acting on scalar functions which are solutions to wave equations. We show that the light ray transform uniquely determines the function in a stable way. The problem is of particular interest because of its connection to inverse problems of the Sachs-Wolfe effect in cosmology.