In relativity and in pseudo-Riemannian geometry, a null hypersurface is a hypersurface whose normal vector at every point is a null vector (has zero length with respect to the local metric tensor).
Another way of saying this is that the pullback of the metric onto the tangent space is degenerate.
For a Lorentzian metric, all the vectors in such a tangent space are space-like except in one direction, in which they are null.
Physically, there is exactly one lightlike worldline contained in a null hypersurface through each point that corresponds to the worldline of a particle moving at the speed of light, and no contained worldlines that are time-like.
Examples of null hypersurfaces include a light cone, a Killing horizon, and the event horizon of a black hole.