# Reconstruction of Lorentzian manifolds from boundary light observation sets

## TL;DR

This paper demonstrates that the topological, differentiable, and conformal structure of certain source subsets in a Lorentzian manifold can be uniquely reconstructed from boundary light observation data, even with complex light ray behaviors.

## Contribution

It provides a constructive method to recover manifold structures from boundary measurements, accommodating conjugate points and multiple reflections.

## Key findings

- Unique reconstruction of manifold structures from boundary light data
- Method handles conjugate points and multiple reflections
- Constructive proof with practical implications

## Abstract

On a time-oriented Lorentzian manifold $(M,g)$ with non-empty boundary satisfying a convexity assumption, we show that the topological, differentiable, and conformal structure of suitable subsets $S\subset M$ of sources is uniquely determined by measurements of the intersection of future light cones from points in $S$ with a fixed open subset of the boundary of $M$; here, light rays are reflected at $\partial M$ according to Snell's law. Our proof is constructive, and allows for interior conjugate points as well as multiply reflected and self-intersecting light cones.