Walker's theorem

Walker's theorem states that in certain mathematical settings, specifically within Lorentzian geometry related to spacetime models in relativity, a Walker structure can be constructed from a particular distribution of subspaces called a parallel null distribution. Essentially, it shows that if a spacetime has a special type of geometric feature—namely, a null (light-like) subspace that remains consistent throughout the space—then the metric (the way distances are measured) can be expressed in a special, simplified form. This facilitates understanding the geometry and physics of such spacetimes by providing a canonical coordinate system reflecting their null structures.