English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Given a Lorentzian manifold, the light ray transform of a function is itsintegrals along null geodesics. This paper is concerned with the injectivity ofthe light ray transform on functions and tensors, up to the natural gauge forthe problem. First, we study the injectivity of the light ray transform of ascalar function on a globally hyperbolic stationary Lorentzian manifold andprove injectivity holds if either a convex foliation condition is satisfied ona Cauchy surface on the manifold or the manifold is real analytic and nullgeodesics do not have cut points. Next, we consider the light ray transform ontensor fields of arbitrary rank in the more restrictive class of staticLorentzian manifolds and show that if the geodesic ray transform on tensorsdefined on the spatial part of the manifold is injective up to the naturalgauge, then the light ray transform on tensors is also injective up to itsnatural gauge. Finally, we provide applications of our results to some inverseproblems about recovery of coefficients for hyperbolic partial differentialequations from boundary data.

The Light Ray transform in Stationary and Static Lorentzian geometries