Geometric description of lightlike foliations by an observer in general relativity

We introduce new concepts and properties of lightlike distributions and foliations (of dimension and co-dimension 1) in a space-time manifold of dimension n, from a purely geometric point of view. Given an observer and a lightlike distribution Ω of dimension or co-dimension 1, its lightlike direction is broken down into two vector fields: a timelike vector field U representing the observer and a spacelike vector field S representing the relative direction of propagation of Ω for this observer. A new distribution Ω− U is defined, with the opposite relative direction of propagation for the observer U . If both distributions Ω and Ω− U are integrable, the pair