Support Theorem for the Light Ray Transform on Minkowski Spaces

TL;DR

This paper proves a support theorem for the Light-Ray transform of vector fields on Minkowski space, showing that vanishing on an open set of light-like geodesics implies certain support properties.

Contribution

It establishes a support theorem for the Light-Ray transform on Minkowski spaces, extending understanding of integral geometry in relativistic settings.

Findings

Support theorem for vector fields vanishing on light-like geodesics

Extension of integral geometry results to Minkowski space

Implications for inverse problems in spacetime geometry

Abstract

We study the Light-Ray transform of integrating vector fields on the Minkowski time-space R^{1+n}, n bigger than equal 2, with the Minkowski metric. We prove a support theorem for vector fields vanishing on an open set of light-like geodesics.